a
    RG5d<                    @   s\  d dl Z d dlmZ d dlmZ d dlmZ d dlmZ d dl	m
Z
 d dlmZmZ d dlmZ d d	lmZ d d
lmZ d dlmZ d dlmZ d dlmZmZmZ d dlmZmZ d dlm Z  d dl!m"Z" d dl#m$Z$ d dl%m&Z&m'Z' d dl(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3 e/Z4e2Z5G dd deZ6ee6dd Z7dd Z8e8Z9dd Z:dS )    N)S)Add)Tuple)FunctionMul)NumberRational)Pow)default_sort_keySymbol)SympifyError)requires_partial)
PRECEDENCE
precedenceprecedence_traditional)Printerprint_function)sstr)has_variety)sympy_deprecation_warning)
prettyForm
stringPict)hobjvobjxobjxsympretty_symbolpretty_atompretty_use_unicodegreek_unicodeUpretty_try_use_unicode	annotatedc                   @   s	  e Zd ZdZdZddddddddddd
Zdd	d
Zdd Zedd Z	dd Z
dd Zdd Zdd ZdddZeZdd Zdd Zdd Zd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ ZeZeZeZeZeZeZeZeZ eZ!d,d- Z"d.d/ Z#d0d1 Z$d2d3 Z%d4d5 Z&d6d7 Z'd8d9 Z(dd:d;Z)d<d= Z*d>d? Z+d@dA Z,dBdC Z-dDdE Z.ddFdGZ/ddHdIZ0dJdK Z1dLdM Z2dNdO Z3dPdQ Z4dRdS Z5dTdU Z6dVdW Z7dXdY Z8dZd[ Z9d\d] Z:d^d_ Z;d`da Z<dbdc Z=ddfdgZ>dhdi Z?djdk Z@dldm ZAdndo ZBdpdq ZCdrds ZDdtdu ZEdvdw ZFdxdy ZGdzd{ ZHd|d} ZId~d ZJdd ZKdd ZLdd ZMdd ZNdd ZOdd ZPdd ZQdd ZRdd ZSdd ZTdd ZUdd ZVdd ZWdd ZXdd ZYdd ZZdd Z[dd Z\i fddZ]dd Z^dd Z_dd Z`dd Zadd Zbdd Zcdd Zddd Zedd ZfdddZgdd Zhdd Zidd Zjdd ZkdddƄZlddȄ Zmddʄ Zndd̄ Zodd΄ ZpdddфZqddӄ ZreddՄ Zsddׄ Ztddل Zuddۄ Zvdd݄ Zwdd߄ Zxdd Zydd Zzdd Z{dd Z|dd Z}dd Z~dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d Zdd Zdd Zdd Zdd	 Zd
d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZdddZd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZeZeZeZdddϐdPdQ dfdRdSZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq ZÐdrds ZĐdtdu ZŐdvdw ZƐdxdy Zǐdzd{ ZȐd|d} Zɐd~d Zʐdd Zːdd Z̐dd Z͐dd Zΐdd Zϐdd ZАdd Zѐdd ZҐdd ZeZԐdd ZՐdd Z֐dd Zאdd Zؐdd Zِdd Zڐdd Zېdd Zܐdd Zݐdd Zސdd Zߐdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddÄ ZdĐdń ZdƐdǄ ZdȐdɄ Zdʐd˄ Zd̐d̈́ Zdΐdτ ZdАdф ZdҐdӄ ZdԐdՄ Zd֐dׄ Zdؐdل Zdڐdۄ ZdS (  PrettyPrinterz?Printer, which converts an expression into 2D ASCII-art figure.Z_prettyNautoTplaini)
order	full_precuse_unicodeZ	wrap_linenum_columnsuse_unicode_sqrt_charroot_notationmat_symbol_styleimaginary_unitperm_cyclicc                 C   sX   t | | t| jd ts2td| jd n"| jd dvrTtd| jd d S )Nr0   z&'imaginary_unit' must a string, not {})r(   jz4'imaginary_unit' must be either 'i' or 'j', not '{}')r   __init__
isinstance	_settingsstr	TypeErrorformat
ValueError)selfsettings r<   X/var/www/html/django/DPS/env/lib/python3.9/site-packages/sympy/printing/pretty/pretty.pyr3   /   s
    zPrettyPrinter.__init__c                 C   s   t t|S Nr   r6   r:   exprr<   r<   r=   emptyPrinter7   s    zPrettyPrinter.emptyPrinterc                 C   s   | j d rdS t S d S )Nr+   T)r5   r    r:   r<   r<   r=   _use_unicode:   s    
zPrettyPrinter._use_unicodec                 C   s   |  |jf i | jS r>   )_printrenderr5   r@   r<   r<   r=   doprintA   s    zPrettyPrinter.doprintc                 C   s   |S r>   r<   r:   er<   r<   r=   _print_stringPictE   s    zPrettyPrinter._print_stringPictc                 C   s   t |S r>   )r   rH   r<   r<   r=   _print_basestringH   s    zPrettyPrinter._print_basestringc                 C   s&   t | |j  }t |d }|S )Natan2)r   
_print_seqargsparensleftr:   rI   pformr<   r<   r=   _print_atan2K   s    zPrettyPrinter._print_atan2Fc                 C   s   t |j|}t|S r>   )r   namer   )r:   rI   Z	bold_nameZsymbr<   r<   r=   _print_SymbolP   s    zPrettyPrinter._print_Symbolc                 C   s   |  || jd dkS )Nr/   bold)rU   r5   rH   r<   r<   r=   _print_MatrixSymbolT   s    z!PrettyPrinter._print_MatrixSymbolc                 C   s,   | j d }|dkr| jdk}tt||dS )Nr*   r&      )r*   )r5   Z_print_levelr   r   )r:   rI   r*   r<   r<   r=   _print_FloatW   s    

zPrettyPrinter._print_Floatc                 C   s~   |j }|j}| |}t|d }t|d }t|| td }t|d }t|| | }t|d }|S )N()MULTIPLICATION SIGNZ_expr1Z_expr2rE   r   rP   rightr"   r:   rI   vec1vec2rR   r<   r<   r=   _print_Cross_   s    
zPrettyPrinter._print_Crossc                 C   s`   |j }| |}t|d }t|d }t|| td }t|| td }|S )NrZ   r[   r\   NABLA_exprrE   r   rP   r^   r"   r:   rI   vecrR   r<   r<   r=   _print_Curlk   s    
zPrettyPrinter._print_Curlc                 C   s`   |j }| |}t|d }t|d }t|| td }t|| td }|S )NrZ   r[   DOT OPERATORrc   rd   rf   r<   r<   r=   _print_Divergencet   s    
zPrettyPrinter._print_Divergencec                 C   s~   |j }|j}| |}t|d }t|d }t|| td }t|d }t|| | }t|d }|S )NrZ   r[   ri   r]   r_   r<   r<   r=   
_print_Dot}   s    
zPrettyPrinter._print_Dotc                 C   sH   |j }| |}t|d }t|d }t|| td }|S )NrZ   r[   rc   rd   r:   rI   funcrR   r<   r<   r=   _print_Gradient   s    
zPrettyPrinter._print_Gradientc                 C   sH   |j }| |}t|d }t|d }t|| td }|S )NrZ   r[   	INCREMENTrd   rl   r<   r<   r=   _print_Laplacian   s    
zPrettyPrinter._print_Laplacianc                 C   s8   zt t|jj| dW S  ty2   | | Y S 0 d S )N)printer)r   r   	__class____name__KeyErrorrB   rH   r<   r<   r=   _print_Atom   s    zPrettyPrinter._print_Atomc                 C   s*   | j r| |S ddg}| |ddS d S )Nz-oooorZ   r[   )rD   ru   rM   )r:   rI   Zinf_listr<   r<   r=   _print_Reals   s    
zPrettyPrinter._print_Realsc                 C   sD   |j d }| |}|jr |js2|js2t|  }t|d }|S Nr   !)rN   rE   
is_Integeris_nonnegative	is_Symbolr   rO   rP   r:   rI   xrR   r<   r<   r=   _print_subfactorial   s    

z!PrettyPrinter._print_subfactorialc                 C   sD   |j d }| |}|jr |js2|js2t|  }t|d }|S rx   rN   rE   rz   r{   r|   r   rO   r^   r}   r<   r<   r=   _print_factorial   s    

zPrettyPrinter._print_factorialc                 C   sD   |j d }| |}|jr |js2|js2t|  }t|d }|S )Nr   z!!r   r}   r<   r<   r=   _print_factorial2   s    

zPrettyPrinter._print_factorial2c                 C   st   |j \}}| |}| |}dt| |  }t|| }t|| }t|dd }|jd d |_|S )N rZ   r[   rX      )rN   rE   maxwidthr   aboverO   baseline)r:   rI   nkZn_pformZk_pformbarrR   r<   r<   r=   _print_binomial   s    


zPrettyPrinter._print_binomialc                 C   sL   t dt|j d }| |j}| |j}t t|||dt ji}|S )Nr   binding)	r   r   rel_oprE   lhsrhsr   nextOPENr:   rI   oplrrR   r<   r<   r=   _print_Relational   s
    zPrettyPrinter._print_Relationalc                 C   s   ddl m}m} | jr|jd }| |}t||rB| j|ddS t||rZ| j|ddS |j	rr|j
srt|  }t|d S | |S d S )Nr   )
EquivalentImpliesu   ⇎)altcharu   ↛   ¬)sympy.logic.boolalgr   r   rD   rN   rE   r4   _print_Equivalent_print_Implies
is_Booleanis_Notr   rO   rP   _print_Function)r:   rI   r   r   argrR   r<   r<   r=   
_print_Not   s    



zPrettyPrinter._print_Notc                 C   s   |j }|rt|j td}|d }| |}|jrB|jsBt|  }|dd  D ]F}| |}|jrt|jstt|  }t|d|  }t|| }qN|S )Nkeyr   rX    %s )	rN   sortedr   rE   r   r   r   rO   r^   )r:   rI   charsortrN   r   rR   	pform_argr<   r<   r=   Z__print_Boolean   s    

zPrettyPrinter.__print_Booleanc                 C   s$   | j r| |dS | j|ddS d S )N   ∧Tr   rD   _PrettyPrinter__print_Booleanr   rH   r<   r<   r=   
_print_And  s    zPrettyPrinter._print_Andc                 C   s$   | j r| |dS | j|ddS d S )Nu   ∨Tr   r   rH   r<   r<   r=   	_print_Or  s    zPrettyPrinter._print_Orc                 C   s$   | j r| |dS | j|ddS d S )Nu   ⊻Tr   r   rH   r<   r<   r=   
_print_Xor  s    zPrettyPrinter._print_Xorc                 C   s$   | j r| |dS | j|ddS d S )Nu   ⊼Tr   r   rH   r<   r<   r=   _print_Nand  s    zPrettyPrinter._print_Nandc                 C   s$   | j r| |dS | j|ddS d S )Nu   ⊽Tr   r   rH   r<   r<   r=   
_print_Nor$  s    zPrettyPrinter._print_Norc                 C   s(   | j r| j||pdddS | |S d S )Nu   →Fr   r   r:   rI   r   r<   r<   r=   r   *  s    zPrettyPrinter._print_Impliesc                 C   s(   | j r| ||pdS | j|ddS d S )Nu   ⇔Tr   r   r   r<   r<   r=   r   0  s    zPrettyPrinter._print_Equivalentc                 C   s(   |  |jd }t|td|  S )Nr   _)rE   rN   r   r   r   r   rQ   r<   r<   r=   _print_conjugate6  s    zPrettyPrinter._print_conjugatec                 C   s$   |  |jd }t|dd }|S )Nr   |)rE   rN   r   rO   rQ   r<   r<   r=   
_print_Abs:  s    zPrettyPrinter._print_Absc                 C   s8   | j r*| |jd }t|dd }|S | |S d S )Nr   lfloorrfloorrD   rE   rN   r   rO   r   rQ   r<   r<   r=   _print_floor?  s
    zPrettyPrinter._print_floorc                 C   s8   | j r*| |jd }t|dd }|S | |S d S )Nr   lceilrceilr   rQ   r<   r<   r=   _print_ceilingG  s
    zPrettyPrinter._print_ceilingc                 C   s  t |jr| jrtd}nd}d }d}t|jD ]p\}}| |}t|| }||7 }|j	rf|dkrv|tt
| }|d u r|}q0t|d }t|| }q0t| |j dtji}	t|}
|dkdkr|
tt
| }
t|
tj| }
|
jd |
_tt|
|	 }
tj|
_|
S )NPARTIAL DIFFERENTIALdr   rX   r   r   F)r   rA   rD   r"   reversedvariable_countrE   r   rP   rz   r6   r^   rO   FUNCbelowr   LINEr   r   MULr   )r:   derivderiv_symbolr~   Zcount_total_derivsymnumsdsfrR   r<   r<   r=   _print_DerivativeO  s8    

zPrettyPrinter._print_Derivativec                 C   s   ddl m}m} || kr.td}t|  S || j}|g kr`| |j	d }t|  S td}|D ],}| t
t|dd}t|| }ql|S )Nr   PermutationCycle rX   ,) sympy.combinatorics.permutationsr   r   r   r   rO   listZcyclic_formrE   sizer6   tuplereplacer^   )r:   dcr   r   ZcycZdc_listr(   r   r<   r<   r=   _print_Cyclet  s    
zPrettyPrinter._print_Cyclec                 C   s   ddl m}m} |j}|d ur8td| ddddd n| jd	d
}|rX| ||S |j}t	t
t|}td}d
}t||D ]P\}	}
| |	}| |
}t|| }|rd}nt|d }t|| }qt|  S )Nr   r   zw
                Setting Permutation.print_cyclic is deprecated. Instead use
                init_printing(perm_cyclic=z).
                z1.6z#deprecated-permutation-print_cyclic   )deprecated_since_versionactive_deprecations_target
stacklevelr1   Tr   Fr   )r   r   r   Zprint_cyclicr   r5   getr   Z
array_formr   rangelenr   ziprE   r   r   rP   r^   rO   )r:   rA   r   r   r1   lowerupperresultfirstur   s1s2colr<   r<   r=   _print_Permutation  s6    


z PrettyPrinter._print_Permutationc                 C   s  |j }| |}|jr"t|  }|}|jD ]:}| |d }| dkrVt|  }t|d| }q,d}d }|jD ]D}	| }
|
d }| j	 }|r|d7 }t
d|}t|}|j||
 d  |_t|	dkrt|	dkrtd}| |	d }t|	dkr | |	d }| |	d }|rntdd|  }t|d	|  }tdd
|  }t|d	|  }t|| }t|| }|st|d	 }|r|}d}qvt|| }qvt|| }tj|_|S )Nr   rX   z dTr   intr      r      F)functionrE   is_Addr   rO   limitsr   r^   heightrD   r   r   r   r   rP   r   r   r   r   )r:   integralr   prettyFr   r~   Z	prettyArgZ	firsttermr   limhH
ascii_modeZvintrR   ZprettyAZprettyBZspcr<   r<   r=   _print_Integral  s\    


zPrettyPrinter._print_Integralc                 C   s  |j }| |}tdd}tdd}tdd}| jrBtdd}d}| }d}d}	d}
|jD ]}| |\}}|d d	 d
 d }|| ||d   | | g}t|d D ]&}|d| d|d   | d  qt	d}t
|j|  }t|	| }	|r| }
t
|| }t
|| }|r4d|_d}| }t	d}t
|jdg|d    }t
|| }t
|| }q\|	|
d  |_t
j|_|S )Nr   rX   r   -u   ┬Tr   r      r   r   r   F)termrE   r   rD   r   r   '_PrettyPrinter__print_SumProduct_Limitsr   appendr   r   stackr   r   r   r   r^   r   r   )r:   rA   rm   Zpretty_funcZhorizontal_chrZ
corner_chrZvertical_chrZfunc_heightr   	max_uppersign_heightr   Zpretty_lowerZpretty_upperr   Z
sign_linesr   Zpretty_signr   paddingr<   r<   r=   _print_Product  sH    




$zPrettyPrinter._print_Productc                    s4    fdd}  |d }||d |d }||fS )Nc                    s>   t dtd d } | } |}t t||| }|S )Nr   ==)r   r   rE   r   r   )r   r   r   r   r   rR   rC   r<   r=   print_start.  s
    

z<PrettyPrinter.__print_SumProduct_Limits.<locals>.print_startr   r   rX   rE   )r:   r   r  prettyUpperprettyLowerr<   rC   r=   Z__print_SumProduct_Limits-  s    z'PrettyPrinter.__print_SumProduct_Limitsc                 C   sZ  | j  }dd }|j}| |}|jr2t|  }| d }d}d}d}	|jD ]}
| |
\}}t	|| }|||
 |
 |\}}}}td}t|j|  }|r| }	t|| }t|| }|r| j|| d |j  8  _d}td}t|jdg|   }t|| }t|| }qP|s8|nd}||	d  | |_tj|_|S )	Nc              	   S   s  ddd}t | d}|d }|d }| d }g }	|r
|	d| d  |	dd|d    td|D ]"}
|	d	d|
 d||
  f  qh|r|	d
d| d||  f  ttd|D ]"}
|	dd|
 d||
  f  q|	dd|d   d  ||| |	|fS || }|| }tdd}|	d|  td|D ].}
|	dd|
 |d d||
 d  f  q<ttd|D ].}
|	dd|
 |d d||
 d  f  qz|	|d |  ||d|  |	|fS d S )N<^>c                 S   s|   |rt | |kr| S |t |  }|dv s4|tdvr@| d|  S |d }d| }|dkrdd| |  S ||  d|t |   S )N)r
  <r
  r   r   >)r   r   )r   widhowneedhalfleadr<   r<   r=   adjust=  s    z6PrettyPrinter._print_Sum.<locals>.asum.<locals>.adjustr   rX   r   r   z\%s`z%s\%sz%s)%sz%s/%s/r   sumr   r   z%s%s%s   )Nr
  )r   r   r   r   r   )Z	hrequiredr   r   Z	use_asciir  r   r   wmorelinesr(   Zvsumr<   r<   r=   asum<  s6    

  
,,z&PrettyPrinter._print_Sum.<locals>.asumr   Tr   r   Fr   )rD   r   rE   r   r   rO   r   r   r   r   r   r   r   r   r   r   r^   r   r   )r:   rA   r   r  r   r   r   r   r  r  r   r	  r  r   r   Zslines
adjustmentZ
prettySignpadZascii_adjustmentr<   r<   r=   
_print_Sum9  sF    *


zPrettyPrinter._print_Sumc           	      C   s   |j \}}}}| |}t|td kr8t|dd }td}| |}| jr`t|d }nt|d }t|| | }t|dks|t	j
t	jfv rd}n| jrt|d	krd
nd}t|| | }t|| }t||dtji}|S )Nr   rZ   r[   r   u   ─→z->z+-r   +u   ⁺u   ⁻r   )rN   rE   r   r   r   rO   rD   r^   r6   r   InfinityNegativeInfinityr   r   )	r:   r   rI   zz0dirEZLimZLimArgr<   r<   r=   _print_Limit  s$    

zPrettyPrinter._print_Limitc                    s  |}i  t |jD ].}t |jD ]| ||f  |f< q qd}d}dg|j }t |jD ],t fddt |jD pdg|< q`d}t |jD ]}d}t |jD ] |f }	|	 | ksJ | |	  }
|
d }|
| }t|	d|  }	t|	d|  }	|du r&|	}qt|d|  }t||	 }q|du rX|}qt |D ]}t|	d }q`t|	| }q|du rtd	}|S )
zL
        This method factors out what is essentially grid printing.
        r   rX   c                    s   g | ]} |f   qS r<   r   .0r(   ZMsr2   r<   r=   
<listcomp>      z8PrettyPrinter._print_matrix_contents.<locals>.<listcomp>r   Nr   r   )
r   rowscolsrE   r   r   r   r^   rP   r   )r:   rI   Mr(   hsepvsepmaxwDD_rowr   wdeltawleftwrightr   r<   r)  r=   _print_matrix_contents  sF    *


z$PrettyPrinter._print_matrix_contents[]c                 C   s,   |  |}| d |_t||| }|S )Nr   )r7  r   r   r   rO   )r:   rI   lparensrparensr2  r<   r<   r=   _print_MatrixBase  s    
zPrettyPrinter._print_MatrixBasec                 C   sp   |j }|jr\ddlm} t||r4| j|jdddS | |}| d |_	t
|dd S | j|dddS d S )Nr   )BlockMatrixr   )r:  r;  r   )r   is_MatrixExprZ&sympy.matrices.expressions.blockmatrixr=  r4   r<  blocksrE   r   r   r   rO   )r:   rI   matr=  r2  r<   r<   r=   _print_Determinant  s    

z PrettyPrinter._print_Determinantc                 C   s*   | j rd}nd}| j|jd d |dd dS )Nu   ⊗.*c                 S   s   t | td kS Nr   r   r   r~   r<   r<   r=   <lambda>  r+  z4PrettyPrinter._print_TensorProduct.<locals>.<lambda>parenthesizerD   rM   rN   )r:   rA   Zcircled_timesr<   r<   r=   _print_TensorProduct  s    z"PrettyPrinter._print_TensorProductc                 C   s*   | j rd}nd}| j|jd d |dd dS )Nr   z/\c                 S   s   t | td kS rC  rD  rE  r<   r<   r=   rF    r+  z3PrettyPrinter._print_WedgeProduct.<locals>.<lambda>rG  rI  )r:   rA   Zwedge_symbolr<   r<   r=   _print_WedgeProduct  s    z!PrettyPrinter._print_WedgeProductc                 C   s<   |  |j}t|dd }| d |_t|d }|S )NrZ   r[   r   tr)rE   r   r   rO   r   r   rP   )r:   rI   r2  r<   r<   r=   _print_Trace  s
    zPrettyPrinter._print_Tracec                 C   s   ddl m} t|j|rJ|jjrJ|jjrJ| t|jj	d|j|jf  S | |j}t
|  }| j|j|jfddjdddd }t
t||d	t
ji}||_||_|S d S )
Nr   MatrixSymbolz_%d%d, 	delimiterr8  r9  rP   r^   r   )sympy.matricesrO  r4   parentr(   	is_numberr2   rE   r   rT   r   rO   rM   r   r   r   
prettyFunc
prettyArgs)r:   rA   rO  rW  ZprettyIndicesrR   r<   r<   r=   _print_MatrixElement'  s,    
z"PrettyPrinter._print_MatrixElementc                    s   ddl m}  |j}t|j|s0t|  } fdd} j||j|jj	||j
|jjfddjddd	d }tt||d
tji}||_||_|S )Nr   rN  c                    sT   t | } | d dkr| d= | d dkr.d| d< | d |krBd| d< t j| dd S )Nr   rX   r   r   :rQ  )r   r   rM   )r~   dimrC   r<   r=   ppsliceB  s    z1PrettyPrinter._print_MatrixSlice.<locals>.ppslicerP  rQ  r8  r9  rS  r   )rT  rO  rE   rU  r4   r   rO   rM   Zrowslicer,  Zcolslicer-  r   r   r   rW  rX  )r:   mrO  rW  r\  rX  rR   r<   rC   r=   _print_MatrixSlice<  s,    	
z PrettyPrinter._print_MatrixSlicec                 C   sV   |j }| |}ddlm}m} t||sFt||sF|jrFt|  }|td }|S )Nr   rO  r=  T)	r   rE   rT  rO  r=  r4   r>  r   rO   )r:   rA   r@  rR   rO  r=  r<   r<   r=   _print_TransposeW  s    

zPrettyPrinter._print_Transposec                 C   sj   |j }| |}| jr td}ntd}ddlm}m} t||s^t||s^|jr^t|	  }|| }|S )Nu   †r  r   r_  )
r   rE   rD   r   rT  rO  r=  r4   r>  rO   )r:   rA   r@  rR   ZdagrO  r=  r<   r<   r=   _print_Adjointa  s    


zPrettyPrinter._print_Adjointc                 C   s(   |j jdkr| |j d S | |j S )NrX   rX   r   r   )r?  shaperE   )r:   Br<   r<   r=   _print_BlockMatrixo  s    z PrettyPrinter._print_BlockMatrixc                 C   s   d }|j D ]p}| |}|d u r&|}q
| d }t| rZtt|d }| |}ntt|d }tt|| }q
|S )Nr   r    + )rN   rE   Zas_coeff_mmulr   could_extract_minus_signr   r   r   )r:   rA   r   itemrR   coeffr<   r<   r=   _print_MatAddt  s    

zPrettyPrinter._print_MatAddc                 C   s   t |j}ddlm} ddlm} ddlm} t|D ]N\}}t	|t
|||frvt|jdkrvt| |  ||< q6| |||< q6tj| S )Nr   HadamardProduct)KroneckerProductMatAddrX   )r   rN   #sympy.matrices.expressions.hadamardrn  Z$sympy.matrices.expressions.kroneckerro  !sympy.matrices.expressions.mataddrq  	enumerater4   r   r   r   rE   rO   __mul__)r:   rA   rN   rn  ro  rq  r(   ar<   r<   r=   _print_MatMul  s    
zPrettyPrinter._print_MatMulc                 C   s   | j rtdS tdS d S )Nu   𝕀IrD   r   r@   r<   r<   r=   _print_Identity  s    zPrettyPrinter._print_Identityc                 C   s   | j rtdS tdS d S )Nu   𝟘0ry  r@   r<   r<   r=   _print_ZeroMatrix  s    zPrettyPrinter._print_ZeroMatrixc                 C   s   | j rtdS tdS d S )Nu   𝟙1ry  r@   r<   r<   r=   _print_OneMatrix  s    zPrettyPrinter._print_OneMatrixc                 C   s4   t |j}t|D ]\}}| |||< qtj| S r>   )r   rN   rt  rE   r   ru  r:   rA   rN   r(   rv  r<   r<   r=   _print_DotProduct  s    
zPrettyPrinter._print_DotProductc                 C   sL   |  |j}ddlm} t|j|s8|jjr8t|  }||  |j }|S )Nr   rN  )	rE   baserT  rO  r4   r>  r   rO   exp)r:   rA   rR   rO  r<   r<   r=   _print_MatPow  s    zPrettyPrinter._print_MatPowc                    sZ   ddl m  ddlm ddlm | jr4td}nd}| j|j	d d | fddd	S )
Nr   rm  rp  MatMulRingrB  c                    s   t |  fS r>   r4   rE  rn  rq  r  r<   r=   rF    r+  z6PrettyPrinter._print_HadamardProduct.<locals>.<lambda>rG  )
rr  rn  rs  rq  !sympy.matrices.expressions.matmulr  rD   r   rM   rN   r:   rA   delimr<   r  r=   _print_HadamardProduct  s    
z$PrettyPrinter._print_HadamardProductc                 C   sp   | j rtd}n
| d}| |j}| |j}t|jtd k rPt|  }tt	
||dtji}|| S )Nr  .r   r   )rD   r   rE   r  r  r   r   r   rO   r   r   r   )r:   rA   circZpretty_baseZ
pretty_expZpretty_circ_expr<   r<   r=   _print_HadamardPower  s    


z"PrettyPrinter._print_HadamardPowerc                    sH   ddl m  ddlm | jr$d}nd}| j|jd d | fdddS )	Nr   rp  r  u    ⨂ z x c                    s   t |  fS r>   r  rE  rq  r  r<   r=   rF    r+  z7PrettyPrinter._print_KroneckerProduct.<locals>.<lambda>rG  )rs  rq  r  r  rD   rM   rN   r  r<   r  r=   _print_KroneckerProduct  s    z%PrettyPrinter._print_KroneckerProductc                 C   s"   |  |jj}t|dd }|S Nr8  r9  )rE   lamdarA   r   rO   )r:   Xr2  r<   r<   r=   _print_FunctionMatrix  s    z#PrettyPrinter._print_FunctionMatrixc                 C   sT   |j dks:|j |j }}t|t|ddddd}| |S | d| |j S d S )NrX   r%  Fevaluate)r   denr   r
   
_print_MulrE   )r:   rA   r   r  resr<   r<   r=   _print_TransferFunction  s
    

z%PrettyPrinter._print_TransferFunctionc                 C   s>   t |j}t|jD ]\}}t| |  ||< qtj| S r>   )r   rN   rt  r   rE   rO   ru  r  r<   r<   r=   _print_Series  s    
zPrettyPrinter._print_Seriesc                 C   s   ddl m} t|j}g }tt|D ]n\}}t||rrt|jdkrr| |}|	 d |_
|t|   q&| |}|	 d |_
|| q&tj| S )Nr   )MIMOParallelrX   r   )sympy.physics.control.ltir  r   rN   rt  r   r4   r   rE   r   r   r   r   rO   ru  )r:   rA   r  rN   Zpretty_argsr(   rv  
expressionr<   r<   r=   _print_MIMOSeries  s    


zPrettyPrinter._print_MIMOSeriesc                 C   sh   d }|j D ]X}| |}|d u r&|}q
tt| }| d |_tt|d }tt|| }q
|S )Nr   rh  )rN   rE   r   r   r   r   r   )r:   rA   r   rj  rR   r<   r<   r=   _print_Parallel  s    

zPrettyPrinter._print_Parallelc                 C   s   ddl m} d }|jD ]p}| |}|d u r2|}qtt| }| d |_tt|d }t	||rv| d |_tt|| }q|S )Nr   )TransferFunctionMatrixr   rh  rX   )
r  r  rN   rE   r   r   r   r   r   r4   )r:   rA   r  r   rj  rR   r<   r<   r=   _print_MIMOParallel  s    


z!PrettyPrinter._print_MIMOParallelc           
      C   s  ddl m}m} |j|dd|j }}t||r:t|jn|g}t|j|rXt|jjn|jg}t||rt|j|r|g ||R  }nt||rt|j|r|j|kr|| }n|g ||jR  }nzt||rt|j|r||kr|| }n||g|R  }n<||kr|| }n(|j|kr2|| }n|g ||R  }t	t
| | }	|	 d |	_|jdkrt	t
|	d nt	t
|	d }	t	t
|	| | }	| ||	 S )Nr   )TransferFunctionSeriesrX   r   r%  rh   - )sympy.physics.controlr  r  sys1varr4   r   rN   sys2r   r   r   rE   r   r   sign)
r:   rA   r  r  r   tfZnum_arg_listZden_arg_listr  denomr<   r<   r=   _print_Feedback  s:    






zPrettyPrinter._print_Feedbackc                 C   s   ddl m}m} | ||j|j}| |j}tt| }|j	dkrXtt
d| ntt
d| }tt| }d|_tt
|d }| d |_t|td}t|j|r| d	 |_tt|| }|S )
Nr   )
MIMOSeriesr  r%  zI + zI - z-1 r   r   rX   )r  r  r  rE   r  r  r   r   r   r  r^   rO   r   r   ru  r4   )r:   rA   r  r  Zinv_matZplantZ	_feedbackr<   r<   r=   _print_MIMOFeedback=  s     z!PrettyPrinter._print_MIMOFeedbackc                 C   s>   |  |j}| d |_| jr(td nd}t|| }|S )NrX   tauz{t})rE   Z	_expr_matr   r   rD   r!   r   r^   )r:   rA   r@  	subscriptr<   r<   r=   _print_TransferFunctionMatrixO  s
    z+PrettyPrinter._print_TransferFunctionMatrixc                 C   s&  ddl m} | jstd||jkr0t|jjS g }g }t||rP| 	 }n
d|fg}|D ]\}}t
|j	 }|jdd d |D ]n\}	}
|
dkr|d|	j  n@|
d	kr|d
|	j  n&| |
 d }||d |	j  ||	j qq^|d dr |d dd  |d< n$|d drD|d dd  |d< g }dg}g }t|D ]\}}|d d|v rZ|}||| d}d|v rtt|D ]`}d||< || dkr||d  dkr|d | d d ||  ||d d   } qXqnRd|v rX|d}|d	krXd||< |d | d d ||  ||d d   }|||< qZdd |D }tdd |D }d|v rt|D ]8\}}t|dkr|ddt|d   d||< qt|D ]2\}}|t|||   t|D ]}|d t|kr|t|krP|dt|d d	 dt|d     ||| kr|||   |||  d 7  < n0||  || d|d	 t||  d   7  < nT|t|kr|dt|d d	 dt|d     ||  d|d	 d  7  < q qtddd |D S )Nr   )Vectorz:ASCII pretty printing of BasisDependent is not implementedc                 S   s   | d   S Nr   )__str__rE  r<   r<   r=   rF  f  r+  z5PrettyPrinter._print_BasisDependent.<locals>.<lambda>r   rX   r   r%  z(-1) r   rh  r   
u   ⎟u   ⎠c                 S   s   g | ]}| d qS )r  )splitr(  r~   r<   r<   r=   r*    r+  z7PrettyPrinter._print_BasisDependent.<locals>.<listcomp>c                 S   s   g | ]}t |qS r<   )r   r  r<   r<   r=   r*    r+  c                 S   s   g | ]}|d d qS )Nr<   )r(  r   r<   r<   r=   r*    r+  )Zsympy.vectorr  rD   NotImplementedErrorzeror   Z_pretty_formr4   separateitemsr   
componentsr   r   rE   rO   
startswithrt  r   r   r   rfindr   insertr  join)r:   rA   r  o1Zvectstrsr  systemZvectZ
inneritemsr   varg_strlengthsstrsflagr(   partstrZtempstrZparenindexZ
n_newlinespartsr2   r<   r<   r=   _print_BasisDependentV  s    





 



"
$z#PrettyPrinter._print_BasisDependentc           	         sh  ddl m  | dkr&| |d S g gdd t| D  }dd |jD } fdd}tj| D ]}|d	 ||  d
}t| d d	d	D ]}t	||d  |j| k r qh|r|| ||d   nL|| |||d   t	||d  dkr ||| d	 gg|| d	< | }g ||d < qqh|d d }| d dkr^||g}| |S )Nr   ImmutableMatrixr<   c                 S   s   g | ]}g qS r<   r<   r'  r<   r<   r=   r*    r+  z2PrettyPrinter._print_NDimArray.<locals>.<listcomp>c                 S   s   g | ]}t t|qS r<   )r   r   r'  r<   r<   r=   r*    r+  c                    s    | ddS )NFr  r<   rE  r  r<   r=   rF    r+  z0PrettyPrinter._print_NDimArray.<locals>.<lambda>r%  TrX   r   )
Zsympy.matrices.immutabler  rankrE   r   re  	itertoolsproductr   r   )	r:   rA   Z	level_strZshape_rangesr@  Zouter_ievenZback_outer_iZout_exprr<   r  r=   _print_NDimArray  s6    


zPrettyPrinter._print_NDimArrayc              	   C   sr  t |}t d|  }t d|  }d }d }t|D ]\}	}
| |
jd }|
|v s^|r||
jkr|
jrtt |d }ntt |d }|
|v rtt |d }tt || ||
  }d}nd}|
jrt || }t |d|   }t |d|   }n:t || }t |d|   }t |d|   }|
j}q8t|	| }t|
| }|S )Nr   r   r   =TF)r   r   rt  rE   rN   is_upr   r   r^   r   r   )r:   rT   indices	index_mapcentertopbotZlast_valenceZprev_mapr(   r  ZindpicZpictr<   r<   r=   _printer_tensor_indices  s6    z%PrettyPrinter._printer_tensor_indicesc                 C   s    |j d j}| }| ||S r  )rN   rT   get_indicesr  )r:   rA   rT   r  r<   r<   r=   _print_Tensor   s    zPrettyPrinter._print_Tensorc                 C   s,   |j jd j}|j  }|j}| |||S r  )rA   rN   rT   r  r  r  )r:   rA   rT   r  r  r<   r<   r=   _print_TensorElement  s    
z"PrettyPrinter._print_TensorElementc                    sB   |  \}} fdd|D }tj| }|r:t|| S |S d S )Nc                    s8   g | ]0}t |td  k r*t |  n |qS r   r   r   r   rE   rO   r'  rC   r<   r=   r*    s   z0PrettyPrinter._print_TensMul.<locals>.<listcomp>)Z!_get_args_for_traditional_printerr   ru  rP   )r:   rA   r  rN   rR   r<   rC   r=   _print_TensMul  s    

zPrettyPrinter._print_TensMulc                    s    fdd|j D }tj| S )Nc                    s8   g | ]0}t |td  k r*t |  n |qS r   r  r'  rC   r<   r=   r*    s   z0PrettyPrinter._print_TensAdd.<locals>.<listcomp>)rN   r   __add__)r:   rA   rN   r<   rC   r=   _print_TensAdd  s    
zPrettyPrinter._print_TensAddc                 C   s    |j d }|js| }| |S r  )rN   r  rE   )r:   rA   r   r<   r<   r=   _print_TensorIndex   s    
z PrettyPrinter._print_TensorIndexc           	      C   s   | j rtd}nd}d }t|jD ]F}| |}t|| }|d u rL|}q"t|d }t|| }q"t| |j	 dtj
i}t|}t|jdkr|| t|j }t|tj| }|jd |_tt|| }tj|_|S )Nr   r   r   r   rX   )rD   r"   r   	variablesrE   r   rP   r^   rA   rO   r   r   r   r   r   r   r   r   r   )	r:   r   r   r~   variabler   r   r   rR   r<   r<   r=   _print_PartialDerivative&  s0    

z&PrettyPrinter._print_PartialDerivativec                    s  i  t |jD ]Z\}}| |j |df< |jdkrFtd |df< qttd| |j  |df< qd}d}t|j fddtdD }d }tD ]}d }	tdD ]}
 ||
f }|	 ||
 ksJ ||
 |	  }|d }|| }t|d	|  }t|
d	|  }|	d u r(|}	qt|	d	|  }	t|	| }	q|d u rZ|	}qt|D ]}t|d	 }qbt||	 }qt|d
d }| d |_tj|_|S )Nr   T	otherwiserX   zfor r   c                    s(   g | ]  t  fd dtD qS )c                    s   g | ]} |f   qS r<   r&  r'  )Pr2   r<   r=   r*  U  r+  z=PrettyPrinter._print_Piecewise.<locals>.<listcomp>.<listcomp>)r   r   r(  r  Zlen_args)r2   r=   r*  U  s   z2PrettyPrinter._print_Piecewise.<locals>.<listcomp>r   {r   )rt  rN   rE   rA   condr   r^   r   r   r   rP   r   rO   r   r   r   r   )r:   Zpexprr   ecr/  r0  r1  r2  r(   r3  r2   pr4  r5  r6  r   r<   r  r=   _print_PiecewiseF  sP    



zPrettyPrinter._print_Piecewisec                 C   s   ddl m} | ||S )Nr   )	Piecewise)$sympy.functions.elementary.piecewiser  rE   rewrite)r:   Ziter  r<   r<   r=   
_print_ITE~  s    zPrettyPrinter._print_ITEc                 C   sP   d }|D ]2}|}|d u r|}qt |d }t || }q|d u rLtd}|S )NrP  r   )r   r^   r   )r:   r  r2  rv  r  r<   r<   r=   _hprint_vec  s    zPrettyPrinter._hprint_vecr   c           	      C   sj   |r$| j s$| j|d|f|||ddS | j||f|||d}ttd| |jd}| j|||f|||dS )Nr   T)rP   r^   rR  ifascii_nougly)rP   r^   rR  r   )rD   rM   r   r   r   r   )	r:   p1p2rP   r^   rR  r  tmpsepr<   r<   r=   _hprint_vseparator  s    
z PrettyPrinter._hprint_vseparatorc                    s   fdd|j D } fdd|jD } |j}| d |_d }||fD ]8} |}|d u rj|}qNt|d }t|| }qN| d |_t|	d }t|
d } ||}t|dd }| d d }| | d }	td	\}
}}}}td
||  | d
|	|   ||
 d}|
d d }t|	 t|j  }t|
 t|j }|| |_t|
d| }|S )Nc                    s   g | ]}  |qS r<   r  r(  rv  rC   r<   r=   r*    r+  z.PrettyPrinter._print_hyper.<locals>.<listcomp>c                    s   g | ]}  |qS r<   r  r(  brC   r<   r=   r*    r+  r   r   rZ   r[   rX   Fr  r  )apbqrE   argumentr   r   r  r   r   rP   r^   r  rO   r$   r   )r:   rI   r  r  r  r2  r  r3  r   r   sztr   addimgr  r<   rC   r=   _print_hyper  s8    

zPrettyPrinter._print_hyperc                     s  i } fdd|j D |d<  fdd|jD |d<  fdd|jD |d<  fdd|jD |d	<  |j}| d
 |_i }|D ]} || ||< qt	d
D ]}t
|d|f  |d|f  }t	d
D ]`}|||f }	||	  d
 }
||
 |	  }t|	d|
  }	t|	d|  }	|	|||f< qqt|d d|d  }t|d }t|d d|d	  }t|| }| d
 |_t|d }t|d } ||}t|dd }| d
 d }| | d }td\}}}}}td||  | d||   || d} t|j} t|j} t|j} t|j }dd }|||\}}|||\}}t|d| }t|d| }|j| d
 }|dkrt|d|  }t|| }||_t|| }|| |_t|d| }|S )Nc                    s   g | ]}  |qS r<   r  r  rC   r<   r=   r*    r+  z0PrettyPrinter._print_meijerg.<locals>.<listcomp>rd  c                    s   g | ]}  |qS r<   r  r  rC   r<   r=   r*    r+  )r   rX   c                    s   g | ]}  |qS r<   r  r  rC   r<   r=   r*    r+  )rX   r   c                    s   g | ]}  |qS r<   r  r  rC   r<   r=   r*    r+  rc  r   r   rX   r   z  rZ   r[   Gr  r  c                 S   sZ   |   |   }|dkr | |fS |dkr>| t|d|  fS t| d|   |fS d S )Nr   r   )r   r   rP   )r  r  diffr<   r<   r=   r    s    z,PrettyPrinter._print_meijerg.<locals>.adjustrP  )anZaotherbmZbotherrE   r  r   r   r  r   r   r   r   rP   r^   r   r  rO   r$   r   r  r  ) r:   rI   r  r  vpidxr(   r1  r2   r   rP   r^   D1D2r2  r   r   r  r  r   r  r  r  pppqpmpnr  puplhtr  r<   rC   r=   _print_meijerg  sh    "

zPrettyPrinter._print_meijergc                 C   s"   t tdd}|| |jd  S )NExp1rI   r   )r   r   rE   rN   )r:   rI   r  r<   r<   r=   _print_ExpBase  s    zPrettyPrinter._print_ExpBasec                 C   s   t tddS )Nr  rI   )r   r   rH   r<   r<   r=   _print_Exp1$  s    zPrettyPrinter._print_Exp1rZ   r[   c                 C   s   | j |j|j||||dS )N)r   	func_namerP   r^   )_helper_print_functionrm   rN   )r:   rI   r   r  rP   r^   r<   r<   r=   r   '  s    zPrettyPrinter._print_Functionc                 C   s   | j |ddS NCr  r   rH   r<   r<   r=   _print_mathieuc-  s    zPrettyPrinter._print_mathieucc                 C   s   | j |ddS Nr   r!  r"  rH   r<   r<   r=   _print_mathieus0  s    zPrettyPrinter._print_mathieusc                 C   s   | j |ddS )NzC'r!  r"  rH   r<   r<   r=   _print_mathieucprime3  s    z"PrettyPrinter._print_mathieucprimec                 C   s   | j |ddS )NzS'r!  r"  rH   r<   r<   r=   _print_mathieusprime6  s    z"PrettyPrinter._print_mathieusprimerP  c	                 C   s   |rt |td}|s$t|dr$|j}|r8| t|}	nt| |  }	|r| jr^t	d}
nd}
| |
}
tt
|	|
dtji}	t| j||dj||d }tt
|	|dtji}|	|_||_|S )Nr   rs   zModifier Letter Low Ringr  r   rQ  rS  )r   r   hasattrrs   rE   r   r   rO   rD   r   r   r   r   rM   r   rW  rX  )r:   rm   rN   r   r  rR  elementwiserP   r^   rW  r  rX  rR   r<   r<   r=   r  9  s8    



z$PrettyPrinter._helper_print_functionc                 C   s$   |j }|j}|g}| j||dddS )Nr   T)rR  r)  )r   rA   r  )r:   rI   rm   r   rN   r<   r<   r=   _print_ElementwiseApplyFunction^  s    z-PrettyPrinter._print_ElementwiseApplyFunctionc                 C   s   ddl m} ddlm}m} ddlm} ddlm} ddl	m
} ddlm} |td dg|td	 d	g|td
 dg|td dg|td dg|td dg|ddgiS )Nr   )KroneckerDelta)gamma
lowergamma)lerchphi)beta)
DiracDelta)ChideltaGammaPhir.  r,  Betarf  r1  )Z(sympy.functions.special.tensor_functionsr+  'sympy.functions.special.gamma_functionsr,  r-  Z&sympy.functions.special.zeta_functionsr.  Z&sympy.functions.special.beta_functionsr/  Z'sympy.functions.special.delta_functionsr0  'sympy.functions.special.error_functionsr1  r!   )r:   r+  r,  r-  r.  r/  r0  r1  r<   r<   r=   _special_function_classesd  s    z'PrettyPrinter._special_function_classesc                 C   sf   | j D ]L}t||r|j|jkr| jr<t| j | d   S t| j | d   S q|j}tt|S )Nr   rX   )r8  
issubclassrs   rD   r   r   )r:   rA   clsr  r<   r<   r=   _print_FunctionClasst  s    
z"PrettyPrinter._print_FunctionClassc                 C   s
   |  |S r>   )rB   r@   r<   r<   r=   _print_GeometryEntity~  s    z#PrettyPrinter._print_GeometryEntityc                 C   s    | j rtd nd}| j||dS )Nr4  r.  r!  rD   r!   r   r:   rI   r  r<   r<   r=   _print_lerchphi  s    zPrettyPrinter._print_lerchphic                 C   s    | j rtd nd}| j||dS )Netadirichlet_etar!  r=  r>  r<   r<   r=   _print_dirichlet_eta  s    z"PrettyPrinter._print_dirichlet_etac                 C   s\   | j rtd nd}|jd dkrJt| |jd   }t|| }|S | j||dS d S )Ntheta	HeavisiderX   g      ?r   r!  )rD   r!   rN   r   rE   rO   rP   r   )r:   rI   r  rR   r<   r<   r=   _print_Heaviside  s    zPrettyPrinter._print_Heavisidec                 C   s   | j |ddS r$  r"  rH   r<   r<   r=   _print_fresnels  s    zPrettyPrinter._print_fresnelsc                 C   s   | j |ddS r  r"  rH   r<   r<   r=   _print_fresnelc  s    zPrettyPrinter._print_fresnelcc                 C   s   | j |ddS )NZAir!  r"  rH   r<   r<   r=   _print_airyai  s    zPrettyPrinter._print_airyaic                 C   s   | j |ddS )NZBir!  r"  rH   r<   r<   r=   _print_airybi  s    zPrettyPrinter._print_airybic                 C   s   | j |ddS )NzAi'r!  r"  rH   r<   r<   r=   _print_airyaiprime  s    z PrettyPrinter._print_airyaiprimec                 C   s   | j |ddS )NzBi'r!  r"  rH   r<   r<   r=   _print_airybiprime  s    z PrettyPrinter._print_airybiprimec                 C   s   | j |ddS )NWr!  r"  rH   r<   r<   r=   _print_LambertW  s    zPrettyPrinter._print_LambertWc                 C   s   | j |ddS )NZCovr!  r"  rH   r<   r<   r=   _print_Covariance  s    zPrettyPrinter._print_Covariancec                 C   s   | j |ddS )NZVarr!  r"  rH   r<   r<   r=   _print_Variance  s    zPrettyPrinter._print_Variancec                 C   s   | j |ddS )Nr  r!  r"  rH   r<   r<   r=   _print_Probability  s    z PrettyPrinter._print_Probabilityc                 C   s   | j |ddddS )Nr#  r8  r9  )r  rP   r^   r"  rH   r<   r<   r=   _print_Expectation  s    z PrettyPrinter._print_Expectationc                 C   sb   |j }|j}| jrd}nd}t|dkr:|d jr:|d }| |}tt||| |ddiS )Nu    ↦  -> rX   r   r   r  )	rA   	signaturerD   r   	is_symbolrE   r   r   r   )r:   rI   rA   sigarrowZvar_formr<   r<   r=   _print_Lambda  s    
zPrettyPrinter._print_Lambdac                 C   s  |  |j}|jr&tdd |jD s4t|jdkrt|d }t|jdkrht||  |j }n$t|jrt||  |jd  }| jrt|d }nt|d }t|jdkrt||  |j }nt||  |jd  }t|	  }t|
d }|S )	Nc                 s   s   | ]}|t jkV  qd S r>   )r   Zero)r(  r  r<   r<   r=   	<genexpr>  r+  z-PrettyPrinter._print_Order.<locals>.<genexpr>rX   ; r   u    → rR  O)rE   rA   pointanyr   r  r   r^   rD   rO   rP   r:   rA   rR   r<   r<   r=   _print_Order  s$    
zPrettyPrinter._print_Orderc                 C   s   | j r`| |jd |jd  }| |jd }td}t|| }t|d }|| }|S | |jd }| |jd |jd  }| |ddd}|| S d S )Nr   rX   r   r  r  r   )rD   rE   rN   r   r^   rM   )r:   rI   shiftr   r  rR   r<   r<   r=   _print_SingularityFunction  s    z(PrettyPrinter._print_SingularityFunctionc                 C   s    | j rtd nd}| j||dS )Nr5  rf  r!  r=  r>  r<   r<   r=   _print_beta  s    zPrettyPrinter._print_betac                 C   s   d}| j ||dS )NzB'r!  r"  r>  r<   r<   r=   _print_betainc  s    zPrettyPrinter._print_betaincc                 C   s   d}| j ||dS )Nrx  r!  r"  r>  r<   r<   r=   _print_betainc_regularized  s    z(PrettyPrinter._print_betainc_regularizedc                 C   s    | j rtd nd}| j||dS Nr3  r!  r=  r>  r<   r<   r=   _print_gamma  s    zPrettyPrinter._print_gammac                 C   s    | j rtd nd}| j||dS re  r=  r>  r<   r<   r=   _print_uppergamma  s    zPrettyPrinter._print_uppergammac                 C   s    | j rtd nd}| j||dS )Nr,  r-  r!  r=  r>  r<   r<   r=   _print_lowergamma  s    zPrettyPrinter._print_lowergammac                 C   s   | j rt|jdkrttd }| |jd }t|  }| |jd }t|  }|| }t|d }t|| }|S | |jd }t|  }t|td  }|S | 	|S d S )Nr   r2  rX   r   r   )
rD   r   rN   r   r!   rE   rO   r^   rP   r   )r:   rI   rv  r   crR   r<   r<   r=   _print_DiracDelta  s     zPrettyPrinter._print_DiracDeltac                 C   s>   |j d jr4| jr4| td|j d  |j d S | |S )Nr   zE_%srX   )rN   rz   rD   r   r   rH   r<   r<   r=   _print_expint  s    "zPrettyPrinter._print_expintc                 C   sD   t d}t | |j  }t t||dt ji}||_||_|S )Nr1  r   )	r   rM   rN   rO   r   r   r   rW  rX  )r:   rI   rW  rX  rR   r<   r<   r=   
_print_Chi  s    
zPrettyPrinter._print_Chic                 C   s^   |  |jd }t|jdkr$|}n|  |jd }| ||}t|  }t|d }|S )Nr   rX   r#  )rE   rN   r   r  r   rO   rP   )r:   rI   pforma0rR   pforma1r<   r<   r=   _print_elliptic_e$  s    zPrettyPrinter._print_elliptic_ec                 C   s.   |  |jd }t|  }t|d }|S )Nr   K)rE   rN   r   rO   rP   rQ   r<   r<   r=   _print_elliptic_k/  s    zPrettyPrinter._print_elliptic_kc                 C   sJ   |  |jd }|  |jd }| ||}t|  }t|d }|S )Nr   rX   r  )rE   rN   r  r   rO   rP   )r:   rI   rm  rn  rR   r<   r<   r=   _print_elliptic_f5  s    zPrettyPrinter._print_elliptic_fc                 C   s   | j rtd nd}| |jd }| |jd }t|jdkrN| ||}n<| |jd }| j||dd}t|d }t|| }t|  }t|| }|S )NPir   rX   r   Fr  rZ  )	rD   r!   rE   rN   r   r  r   rP   rO   )r:   rI   rT   rm  rn  rR   Zpforma2Zpformar<   r<   r=   _print_elliptic_pi=  s    z PrettyPrinter._print_elliptic_pic                 C   s    | j rttdS | tdS )NphiGoldenRatiorD   r   r   rE   r   r@   r<   r<   r=   _print_GoldenRatioL  s    z PrettyPrinter._print_GoldenRatioc                 C   s    | j rttdS | tdS )Nr,  
EulerGammarx  r@   r<   r<   r=   _print_EulerGammaQ  s    zPrettyPrinter._print_EulerGammac                 C   s   |  tdS )Nr
  )rE   r   r@   r<   r<   r=   _print_CatalanV  s    zPrettyPrinter._print_Catalanc                 C   s\   |  |jd }|jtjkr(t|  }t|d }t||  |jd  }tj|_|S )Nr   z mod rX   )rE   rN   r   r   r   rO   r^   r   r^  r<   r<   r=   
_print_ModY  s    zPrettyPrinter._print_Modc                 C   s  | j ||d}g g  }}dd }t|D ]\}}|jr| r|jdd\}	}
|	dkrft|
ddi}nt|	 g|
R ddi}| |}|||| q(|jr|j	dkr|d  || q(|j
r|d	k r| | }|||| q(|jr|t| |   q(|| | q(|rd
}|D ]$}|d ur.| dkr. qXq.d}|D ]p}|| d }}|d	k r| d
 }}|rtt|jtt|j	 }n
| |}|r|||}|||< q\tj| S )Nr)   c                 S   sj   |dkr |   dkrd}q$d}nd}| jtjks<| jtjkrJt|   }n| }t||}t|dtjiS )z'Prepend a minus sign to a pretty form. r   rX   z- r   r  r   )r   r   r   NEGADDr   rO   r   )rR   r  Z	pform_negr  r<   r<   r=   pretty_negativef  s    
z1PrettyPrinter._print_Add.<locals>.pretty_negativeF)rationalr%  r  rX   r   T)Z_as_ordered_termsrt  is_Mulri  as_coeff_mulr   rE   r   is_Rationalq	is_Numberis_Relationalr   rO   r   r6   r  r  )r:   rA   r)   termspformsr  r  r(   r   rk  otherZnegtermrR   largenegativer<   r<   r=   
_print_Addb  sJ    






zPrettyPrinter._print_Addc           	         s  ddl m  |j}|d tju s:tdd |dd  D rttj|}|d dk}|rjt	ddd|d< t	j
| }|rt	d|j |j|j}|S g }g }jd	vr| }n
t|j}t| fd
dd}|D ]}|jr8|jr8|jjr8|jjr8|jdkr |t|j|j dd n|t|j|j  q|jr|tjur|jdkrh|t|j |jdkr|t|j q|| qЇfdd|D }fdd|D }t|dkrt	j
| S t|dkr|tj t	j
| t	j
|  S d S )Nr   Quantityc                 s   s   | ]}t |tV  qd S r>   )r4   r   r(  r   r<   r<   r=   rY    r+  z+PrettyPrinter._print_Mul.<locals>.<genexpr>rX   z-1r}  r   )oldnonec                    s    t |  pt | tot | j S r>   )r4   r
   r  rE  r  r<   r=   rF    s   
z*PrettyPrinter._print_Mul.<locals>.<lambda>r   r%  Fr  c                    s   g | ]}  |qS r<   r  )r(  airC   r<   r=   r*    r+  z,PrettyPrinter._print_Mul.<locals>.<listcomp>c                    s   g | ]}  |qS r<   r  )r(  birC   r<   r=   r*    r+  )Zsympy.physics.unitsr  rN   r   Oner]  r   maprE   r   ru  r   r   r   r)   as_ordered_factorsr   is_commutativeis_Powr  r  is_negativer   r
   r  r  r  r	   r  r   )	r:   r  rN   ZstrargsZnegoneobjrv  r   rj  r<   )r  r:   r=   r    sF    (



$
zPrettyPrinter._print_Mulc           	         st  |  |}| jd rT| jrT|dkrT| dkrT| dksF|jrT|jrTt|d S t	dd t	dd  }|  |}| dkr|  ||  d|  S |dkrdnt
|d}t|dkrdt|d  | }t|d	 | }d
|_| d td	 fddtD }d |_t|| }td|j|_ttdd|  }t|| }t|| }|S )Nr-   r   rX   u   √r  \r   r   r  r   c                 3   s*   | ]"}d | d    d |  V  qdS )r   rX   Nr<   r'  Z_zZZ
linelengthr<   r=   rY    s   z0PrettyPrinter._print_nth_root.<locals>.<genexpr>r   )rE   r5   rD   r   r   rz   r{   r   rP   r   r6   ljustr   r   r   r  r   r^   r   r   r   )	r:   r  rootZbprettyZrootsignZrprettyr  diagonalr   r<   r  r=   _print_nth_root  sD    






zPrettyPrinter._print_nth_rootc                 C   s   ddl m} | \}}|jr|tju r:td| | S ||\}}|tju r~|j	r~|j
s~|jsh|jr~| jd r~| ||S |jr|dk rtd| t|| dd S |jrt| |  | |S | || | S )Nr   )fractionr}  r.   Fr  )sympy.simplify.simplifyr  as_base_expr  r   NegativeOner   rE   r  is_Atomrz   r  r|   r5   r  r
   r  rO   __pow__)r:   powerr  r   rI   r   r   r<   r<   r=   
_print_Pow  s    
"zPrettyPrinter._print_Powc                 C   s   |  |jd S r  )rE   rN   r@   r<   r<   r=   _print_UnevaluatedExpr%  s    z$PrettyPrinter._print_UnevaluatedExprc                 C   s   |dkr0|dk r"t t|t jdS t t|S n\t|dkrt|dkr|dk rnt t|t jdt t| S t t|t t| S nd S d S )NrX   r   )r   
   )r   r6   r  abs)r:   r  r  r<   r<   r=   Z__print_numer_denom(  s    z!PrettyPrinter.__print_numer_denomc                 C   s*   |  |j|j}|d ur|S | |S d S r>   )!_PrettyPrinter__print_numer_denomr  r  rB   r:   rA   r   r<   r<   r=   _print_Rational:  s    zPrettyPrinter._print_Rationalc                 C   s*   |  |j|j}|d ur|S | |S d S r>   )r  	numeratordenominatorrB   r  r<   r<   r=   _print_FractionB  s    zPrettyPrinter._print_Fractionc                 C   sh   t |jdkr8t|js8| |jd | t |j S | jrBdnd}| j|jd d d| dd dS d S )	NrX   r      ×r~   r   c                 S   s   | j p| jp| jS r>   )is_Unionis_Intersectionis_ProductSetsetr<   r<   r=   rF  P  s   z1PrettyPrinter._print_ProductSet.<locals>.<lambda>rG  )r   setsr   rE   rD   rM   )r:   r  Z	prod_charr<   r<   r=   _print_ProductSetJ  s     zPrettyPrinter._print_ProductSetc                 C   s   t |jtd}| |dddS )Nr   r  }rP  )r   rN   r   rM   )r:   r   r  r<   r<   r=   _print_FiniteSetS  s    zPrettyPrinter._print_FiniteSetc                 C   s   | j rd}nd}|jjrH|jjrH|jjr8|ddd|f}q|ddd|f}n||jjrj||d |j |d f}nZ|jjrt|}t|t||f}n6t|dkrt|}t|t|||d f}nt	|}| 
|ddd	S )
N   …...r%  r   rX   r   r  r  rP  )rD   startis_infinitestopstepis_positiveiterr   r   r   rM   )r:   r   dotsprintsetitr<   r<   r=   _print_RangeW  s"    zPrettyPrinter._print_Rangec                 C   s`   |j |jkr$| |jd d ddS |jr0d}nd}|jr@d}nd}| |jd d ||S d S )	NrX   r  r  rZ   r8  r[   r9  r   )r  endrM   rN   Z	left_openZ
right_openr:   r(   rP   r^   r<   r<   r=   _print_Intervalp  s    zPrettyPrinter._print_Intervalc                 C   s    d}d}|  |jd d ||S )Nr  r  r   rM   rN   r  r<   r<   r=   _print_AccumulationBounds  s    z'PrettyPrinter._print_AccumulationBoundsc                 C   s(   dt dd }| j|jd d |dd dS )Nr   Intersectionr   c                 S   s   | j p| jp| jS r>   )r  r  is_Complementr  r<   r<   r=   rF    s   z3PrettyPrinter._print_Intersection.<locals>.<lambda>rG  r   rM   rN   r:   r   rR  r<   r<   r=   _print_Intersection  s    z!PrettyPrinter._print_Intersectionc                 C   s(   dt dd }| j|jd d |dd dS )Nr   Unionr"   c                 S   s   | j p| jp| jS r>   )r  r  r  r  r<   r<   r=   rF    s   z,PrettyPrinter._print_Union.<locals>.<lambda>rG  r  )r:   r   Zunion_delimiterr<   r<   r=   _print_Union  s    zPrettyPrinter._print_Unionc                 C   s,   | j stddtd }| |jd d |S )Nz?ASCII pretty printing of SymmetricDifference is not implementedr   SymmetricDifference)rD   r  r   rM   rN   )r:   r   Zsym_delimeterr<   r<   r=   _print_SymmetricDifference  s    z(PrettyPrinter._print_SymmetricDifferencec                 C   s   d}| j |jd d |dd dS )Nz \ c                 S   s   | j p| jp| jS r>   )r  r  r  r  r<   r<   r=   rF    s   z1PrettyPrinter._print_Complement.<locals>.<lambda>rG  r  r  r<   r<   r=   _print_Complement  s    zPrettyPrinter._print_Complementc                    s   | j rd nd |j}|j}|j}| |j}t|dkrl| j|d  |d fdd}| j||ddd	dd
S t	 fddt
||D }| j|d d dd}| j||ddd	dd
S d S )N   ∊inrX   r   r   rQ  r  r  TrP   r^   r  rR  c                 3   s,   | ]$\}}|d  d |dfD ]
}|V  qqdS )r   rP  Nr<   )r(  r  Zsetvr2   innr<   r=   rY    s   
z0PrettyPrinter._print_ImageSet.<locals>.<genexpr>r%  r   )rD   r  Z	base_setsrS  rE   rA   r   rM   r  r   r   )r:   tsfunr  rS  rA   r   Zpargsr<   r  r=   _print_ImageSet  s*    zPrettyPrinter._print_ImageSetc           	      C   s   | j rd}d}nd}d}| t|j}t|jdd }|d urP| |j }n(| |j}| j rx| |}t|	  }|j
tju r| j||dddd	d
S | |j
}| j|||||fd	d}| j||dddd	d
S )Nr  r   r  andas_exprr  r  Tr   r  rQ  )rD   rM   r   r   getattr	conditionrE   r  r   rO   Zbase_setr   UniversalSetr  )	r:   r  r  _andr  r  r  r  r   r<   r<   r=   _print_ConditionSet  s2    

z!PrettyPrinter._print_ConditionSetc                 C   s^   | j rd}nd}| |j}| |j}| |j}| j|||fdd}| j||dddddS )	Nr  r  r   rQ  r  r  Tr  )rD   rM   r  rE   rA   r  r  )r:   r  r  r  rA   Zprodsetsr   r<   r<   r=   _print_ComplexRegion  s    z"PrettyPrinter._print_ComplexRegionc                 C   sH   |j \}}| jr8d}tt| ||| |ddiS tt|S d S )Nu    ∈ r   r  )rN   rD   r   r   r   rE   r   )r:   rI   r  r  elr<   r<   r=   _print_Contains  s    

zPrettyPrinter._print_Containsc                 C   sP   |j jtju r(|jjtju r(| |jS | jr4d}nd}| |	 | | S )Nr  r  )
r  Zformular   rX  bnrE   a0rD   r  truncate)r:   r   r  r<   r<   r=   _print_FourierSeries  s    z"PrettyPrinter._print_FourierSeriesc                 C   s   |  |jS r>   )r  infiniter:   r   r<   r<   r=   _print_FormalPowerSeries	  s    z&PrettyPrinter._print_FormalPowerSeriesc                 C   s0   t | |j  }| td}t || S )NZSetExpr)r   rE   r  rO   r   r^   )r:   seZ
pretty_setpretty_namer<   r<   r=   _print_SetExpr	  s    zPrettyPrinter._print_SetExprc                 C   s   | j rd}nd}t|jjdks0t|jjdkr8td|jtju r~|j}|||d ||d ||d ||f}n>|jtj	u s|j
dkr|d d }|| t|}nt|}| |S )	Nr  r  r   z@Pretty printing of sequences with symbolic bound not implementedr   r   rX   r   )rD   r   r  free_symbolsr  r  r   r  rk  r  lengthr   r   _print_list)r:   r   r  r  r  r<   r<   r=   _print_SeqFormula	  s      

zPrettyPrinter._print_SeqFormulac                 C   s   dS )NFr<   rE  r<   r<   r=   rF  %	  r+  zPrettyPrinter.<lambda>c              	   C   s   zdg }|D ]:}|  |}	||r,t|	  }	|r:|| ||	 q
|sTtd}
nttj|  }
W n| ty   d }
|D ]P}| |}	||rt|	  }	|
d u r|	}
qztt|
| }
tt|
|	 }
qz|
d u rtd}
Y n0 t|
j|||d }
|
S )Nr   rt  )rE   r   rO   r   r   r   AttributeErrorrG   )r:   seqrP   r^   rR  rH  r  r  rj  rR   r   r<   r<   r=   rM   $	  s4    



zPrettyPrinter._print_seqc                 C   sP   d }|D ].}|d u r|}qt || }t || }q|d u rHt dS |S d S )Nr   )r   r^   )r:   rR  rN   rR   r   r<   r<   r=   r  M	  s    zPrettyPrinter.joinc                 C   s   |  |ddS r  rM   )r:   r   r<   r<   r=   r  \	  s    zPrettyPrinter._print_listc                 C   sL   t |dkr:tt| |d d }t|jdddd S | |ddS d S )NrX   r   r   rZ   r[   Trt  )r   r   r   r   rE   rO   rM   )r:   r  Zptupler<   r<   r=   _print_tuple_	  s    zPrettyPrinter._print_tuplec                 C   s
   |  |S r>   )r  r@   r<   r<   r=   _print_Tuplef	  s    zPrettyPrinter._print_Tuplec                 C   s`   t | td}g }|D ]8}| |}| || }tt|d| }|| q| |ddS )Nr   z: r  r  )	r   keysr   rE   r   r   r   r   rM   )r:   r   r  r  r   rp  Vr   r<   r<   r=   _print_dicti	  s    
zPrettyPrinter._print_dictc                 C   s
   |  |S r>   )r   )r:   r   r<   r<   r=   _print_Dictv	  s    zPrettyPrinter._print_Dictc                 C   s:   |st dS t|td}| |}t |jdddd }|S )Nzset()r   r  r  Trt  )r   r   r   rM   rO   r:   r   r  prettyr<   r<   r=   
_print_sety	  s    
zPrettyPrinter._print_setc                 C   sd   |st dS t|td}| |}t |jdddd }t |jdddd }t tt|j| }|S )	Nzfrozenset()r   r  r  Trt  rZ   r[   )	r   r   r   rM   rO   r   r   typers   r  r<   r<   r=   _print_frozenset	  s    
zPrettyPrinter._print_frozensetc                 C   s   | j rtdS tdS d S )Nu   𝕌r  ry  r  r<   r<   r=   _print_UniversalSet	  s    z!PrettyPrinter._print_UniversalSetc                 C   s   t t|S r>   r   r   )r:   ringr<   r<   r=   _print_PolyRing	  s    zPrettyPrinter._print_PolyRingc                 C   s   t t|S r>   r  )r:   fieldr<   r<   r=   _print_FracField	  s    zPrettyPrinter._print_FracFieldc                 C   s   t t|S r>   r?   )r:   elmr<   r<   r=   _print_FreeGroupElement	  s    z%PrettyPrinter._print_FreeGroupElementc                 C   s   t t|S r>   r  )r:   polyr<   r<   r=   _print_PolyElement	  s    z PrettyPrinter._print_PolyElementc                 C   s   t t|S r>   r  )r:   fracr<   r<   r=   _print_FracElement	  s    z PrettyPrinter._print_FracElementc                 C   s*   |j r| |  S | | S d S r>   )
is_aliasedrE   as_polyr  r@   r<   r<   r=   _print_AlgebraicNumber	  s    z$PrettyPrinter._print_AlgebraicNumberc                 C   s:   | j |jdd|jg}t| |  }t|d }|S )Nlexr~  CRootOf)r  rA   r  r   rM   rO   rP   r:   rA   rN   rR   r<   r<   r=   _print_ComplexRootOf	  s    z"PrettyPrinter._print_ComplexRootOfc                 C   sT   | j |jddg}|jtjur0|| |j t| |	  }t|
d }|S )Nr  r~  RootSum)r  rA   r  r   IdentityFunctionr   rE   r   rM   rO   rP   r  r<   r<   r=   _print_RootSum	  s    zPrettyPrinter._print_RootSumc                 C   s"   | j rd}nd}tt||j S )Nu   ℤ_%dzGF(%d))rD   r   r   mod)r:   rA   formr<   r<   r=   _print_FiniteField	  s    z PrettyPrinter._print_FiniteFieldc                 C   s   | j rtdS tdS d S )Nu   ℤZZry  r@   r<   r<   r=   _print_IntegerRing	  s    z PrettyPrinter._print_IntegerRingc                 C   s   | j rtdS tdS d S )Nu   ℚQQry  r@   r<   r<   r=   _print_RationalField	  s    z"PrettyPrinter._print_RationalFieldc                 C   s>   | j rd}nd}|jrt|S | t|d t|j S d S )Nu   ℝRRr   rD   has_default_precisionr   rE   r   r6   	precisionr:   domainprefixr<   r<   r=   _print_RealField	  s    zPrettyPrinter._print_RealFieldc                 C   s>   | j rd}nd}|jrt|S | t|d t|j S d S )Nu   ℂCCr   r%  r(  r<   r<   r=   _print_ComplexField	  s    z!PrettyPrinter._print_ComplexFieldc                 C   s^   t |j}|jjs6ttd| |j }|| | |dd}t|	| |j
 }|S Norder=r8  r9  r   symbolsr)   
is_defaultr   r^   rE   r   rM   rP   r)  r:   rA   rN   r)   rR   r<   r<   r=   _print_PolynomialRing	  s    

z#PrettyPrinter._print_PolynomialRingc                 C   s^   t |j}|jjs6ttd| |j }|| | |dd}t|	| |j
 }|S )Nr/  rZ   r[   r0  r3  r<   r<   r=   _print_FractionField	  s    

z"PrettyPrinter._print_FractionFieldc                 C   sV   |j }t|jt|jkr.|dt|j f }| |dd}t|| |j }|S r.  )	r1  r6   r)   Zdefault_orderrM   r   rP   rE   r)  )r:   rA   grR   r<   r<   r=   _print_PolynomialRingBase	  s    z'PrettyPrinter._print_PolynomialRingBasec                    s    fdd j D }td|jddd }fdd jD }ttd j }ttd	 j }d|g| ||g }t|  }t|	 j
j }|S )
Nc                    s   g | ]}j | jd qS )r~  )r  r)   r  basisr:   r<   r=   r*  
  s   z6PrettyPrinter._print_GroebnerBasis.<locals>.<listcomp>rP  r8  r9  rS  c                    s   g | ]}  |qS r<   r  )r(  genrC   r<   r=   r*  
  r+  zdomain=r/  )exprsr   r  rO   gensr^   rE   r)  r)   rP   rr   rs   )r:   r9  r;  r<  r)  r)   rR   r<   r8  r=   _print_GroebnerBasis
  s    z"PrettyPrinter._print_GroebnerBasisc              	      s     |j}t|  }| dkr,| nd}ttd||jd}t|| }|j}| d |_t| 	 fddt
|j|jD  }||_|S )NrX   r   r   r  c              	      s8   g | ]0} j  |d  td |d fddqS )r   r  rX   r   rQ  )rM   rE   r   )r(  r  rC   r<   r=   r*  
  s   $z-PrettyPrinter._print_Subs.<locals>.<listcomp>)rE   rA   r   rO   r   r   r   r   r^   rM   r   r  r\  )r:   rI   rR   r   Zrvertr   r<   rC   r=   _print_Subs
  s    zPrettyPrinter._print_Subsc           
      C   s   t |}| |jd }t d|  }t || }t || }t|jdkrV|S |j\}}|}t | |g  }	t t	
||	dt ji}||_|	|_|S )Nr   r   rX   r   )r   rE   rN   r   r   r^   r   rM   rO   r   r   r   rW  rX  )
r:   rI   rT   rR   r   r   r]  r~   rW  rX  r<   r<   r=   _print_number_function&
  s$    

z$PrettyPrinter._print_number_functionc                 C   s   |  |dS )Nr#  r?  rH   r<   r<   r=   _print_euler:
  s    zPrettyPrinter._print_eulerc                 C   s   |  |dS )Nr   r@  rH   r<   r<   r=   _print_catalan=
  s    zPrettyPrinter._print_catalanc                 C   s   |  |dS )Nrf  r@  rH   r<   r<   r=   _print_bernoulli@
  s    zPrettyPrinter._print_bernoullic                 C   s   |  |dS )NLr@  rH   r<   r<   r=   _print_lucasE
  s    zPrettyPrinter._print_lucasc                 C   s   |  |dS )Nr  r@  rH   r<   r<   r=   _print_fibonacciH
  s    zPrettyPrinter._print_fibonaccic                 C   s   |  |dS )Nr`  r@  rH   r<   r<   r=   _print_tribonacciK
  s    zPrettyPrinter._print_tribonaccic                 C   s"   | j r| |dS | |dS d S )Nu   γ	stieltjes)rD   r?  rH   r<   r<   r=   _print_stieltjesN
  s    zPrettyPrinter._print_stieltjesc                 C   s   |  |jd }t|td }t||  |jd  }| jrPttd}ntd}|}t|d|   }t|d|   }t|	|dtj
iS )Nr   r   rX   r2  r   r   r   )rE   rN   r   r^   rD   r   r   rP   r   r   POW)r:   rI   rR   rv  r   r  r  r<   r<   r=   _print_KroneckerDeltaT
  s    z#PrettyPrinter._print_KroneckerDeltac                 C   s   t |dr0| d}t|| |  }|S t |dr| d}t|| |j }t|| d }t|| |j }|S t |dr| d}t|| |j }|S | d S d S )N
as_booleanzDomain: r  z in r1  z
Domain on )r(  rE   r   r^   rL  r1  r  )r:   r   rR   r<   r<   r=   _print_RandomDomaina
  s    





z!PrettyPrinter._print_RandomDomainc                 C   sD   z"|j d ur | |j |W S W n ty4   Y n0 | t|S r>   )r	  rE   to_sympyr   reprr:   r  r<   r<   r=   
_print_DMPs
  s    
zPrettyPrinter._print_DMPc                 C   s
   |  |S r>   )rQ  rP  r<   r<   r=   
_print_DMF|
  s    zPrettyPrinter._print_DMFc                 C   s   |  t|jS r>   rE   r   rT   )r:   objectr<   r<   r=   _print_Object
  s    zPrettyPrinter._print_Objectc                 C   s8   t d}| |j}| |j}|||d }t|S )Nz-->r   )r   rE   r)  codomainr^   r   )r:   morphismrV  r)  rV  tailr<   r<   r=   _print_Morphism
  s
    zPrettyPrinter._print_Morphismc                 C   s.   |  t|j}| |}t|d|d S )NrZ  r   )rE   r   rT   rY  r   r^   )r:   rW  r  pretty_morphismr<   r<   r=   _print_NamedMorphism
  s    
z"PrettyPrinter._print_NamedMorphismc                 C   s"   ddl m} | ||j|jdS )Nr   )NamedMorphismid)Zsympy.categoriesr\  r[  r)  rV  )r:   rW  r\  r<   r<   r=   _print_IdentityMorphism
  s    z%PrettyPrinter._print_IdentityMorphismc                 C   sT   t d}dd |jD }|  ||d }| |}| |}t||d S )Nr  c                 S   s   g | ]}t |jqS r<   )r   rT   )r(  	componentr<   r<   r=   r*  
  s   z:PrettyPrinter._print_CompositeMorphism.<locals>.<listcomp>rZ  r   )r   r  reverser  rE   rY  r   r^   )r:   rW  ZcircleZcomponent_names_listcomponent_namesr  rZ  r<   r<   r=   _print_CompositeMorphism
  s    

z&PrettyPrinter._print_CompositeMorphismc                 C   s   |  t|jS r>   rS  )r:   categoryr<   r<   r=   _print_Category
  s    zPrettyPrinter._print_Categoryc                 C   sX   |j s| tjS | |j }|jrLdtd }| |jd }|||}t|d S )Nr   z==>r   )ZpremisesrE   r   EmptySetZconclusionsr   r^   r   )r:   diagramZpretty_resultZresults_arrowZpretty_conclusionsr<   r<   r=   _print_Diagram
  s    zPrettyPrinter._print_Diagramc                    s2   ddl m} | fddt jD }| |S )Nr   )Matrixc                    s&   g | ]  fd dt jD qS )c                    s,   g | ]$} |f r  |f nt d qS )r   r   )r(  r2   )gridr(   r<   r=   r*  
  s   z?PrettyPrinter._print_DiagramGrid.<locals>.<listcomp>.<listcomp>)r   r   r  ri  )r(   r=   r*  
  s   z4PrettyPrinter._print_DiagramGrid.<locals>.<listcomp>)rT  rh  r   r   r7  )r:   ri  rh  matrixr<   rj  r=   _print_DiagramGrid
  s
    z PrettyPrinter._print_DiagramGridc                 C   s   |  |ddS r  r  r:   r]  r<   r<   r=   _print_FreeModuleElement
  s    z&PrettyPrinter._print_FreeModuleElementc                 C   s   |  |jddS )Nr  r  )rM   r<  r:   r.  r<   r<   r=   _print_SubModule
  s    zPrettyPrinter._print_SubModulec                 C   s   |  |j|  |j S r>   )rE   r	  r  ro  r<   r<   r=   _print_FreeModule
  s    zPrettyPrinter._print_FreeModulec                 C   s   |  dd |jjD ddS )Nc                 S   s   g | ]
\}|qS r<   r<   r  r<   r<   r=   r*  
  r+  z?PrettyPrinter._print_ModuleImplementedIdeal.<locals>.<listcomp>r  r  )rM   _moduler<  ro  r<   r<   r=   _print_ModuleImplementedIdeal
  s    z+PrettyPrinter._print_ModuleImplementedIdealc                 C   s   |  |j|  |j S r>   )rE   r	  
base_idealr:   Rr<   r<   r=   _print_QuotientRing
  s    z!PrettyPrinter._print_QuotientRingc                 C   s   |  |j|  |jj S r>   )rE   datar	  rt  ru  r<   r<   r=   _print_QuotientRingElement
  s    z(PrettyPrinter._print_QuotientRingElementc                 C   s   |  |j|  |jj S r>   )rE   rx  modulekilled_modulerm  r<   r<   r=   _print_QuotientModuleElement
  s    z*PrettyPrinter._print_QuotientModuleElementc                 C   s   |  |j|  |j S r>   )rE   r  r{  ro  r<   r<   r=   _print_QuotientModule
  s    z#PrettyPrinter._print_QuotientModulec              	   C   sN   |  | }| d |_t|d|  |jdtdd |  |j }|S )Nr   z : z %s> r   )	rE   Z_sympy_matrixr   r   r   r^   r)  r   rV  )r:   r   rk  rR   r<   r<   r=   _print_MatrixHomomorphism
  s    z'PrettyPrinter._print_MatrixHomomorphismc                 C   s   |  |jS r>   rE   rT   )r:   Zmanifoldr<   r<   r=   _print_Manifold
  s    zPrettyPrinter._print_Manifoldc                 C   s   |  |jS r>   r  )r:   patchr<   r<   r=   _print_Patch
  s    zPrettyPrinter._print_Patchc                 C   s   |  |jS r>   r  )r:   coordsr<   r<   r=   _print_CoordSystem
  s    z PrettyPrinter._print_CoordSystemc                 C   s   |j j|j j}| t|S r>   )
_coord_sysr1  _indexrT   rE   r   )r:   r  stringr<   r<   r=   _print_BaseScalarField
  s    z$PrettyPrinter._print_BaseScalarFieldc                 C   s*   t dd |jj|j j }| t|S )Nr   r   )r"   r  r1  r  rT   rE   r   )r:   r  r   r<   r<   r=   _print_BaseVectorField
  s    z$PrettyPrinter._print_BaseVectorFieldc                 C   sn   | j rd}nd}|j}t|drF|jj|j j}| |d t| S | |}t	|
  }t	|| S d S )Nu   ⅆr   r  r   )rD   Z_form_fieldr(  r  r1  r  rT   rE   r   r   rO   rP   )r:   r  r   r  r  rR   r<   r<   r=   _print_Differential
  s    

z!PrettyPrinter._print_Differentialc                 C   s8   |  |jd }t|d|jj  }t|d }|S )Nr   z%s(r[   )rE   rN   r   rP   rr   rs   r^   )r:   r  rR   r<   r<   r=   	_print_Tr
  s    zPrettyPrinter._print_Trc                 C   sH   |  |jd }t|  }| jr6t|td  }nt|d }|S )Nr   nurE   rN   r   rO   rD   rP   r!   rQ   r<   r<   r=   _print_primenu  s    zPrettyPrinter._print_primenuc                 C   sH   |  |jd }t|  }| jr6t|td  }nt|d }|S )Nr   Omegar  rQ   r<   r<   r=   _print_primeomega  s    zPrettyPrinter._print_primeomegac                 C   s(   |j j dkr| d}|S | |S d S )Ndegree   °)rT   rE   rB   rQ   r<   r<   r=   _print_Quantity  s    
zPrettyPrinter._print_Quantityc                 C   sD   t dt|j d }| |j}| |j}t t||| }|S )Nr   )r   r   r   rE   r   r   r   r   r   r<   r<   r=   _print_AssignmentBase  s
    z#PrettyPrinter._print_AssignmentBasec                 C   s   |  |jS r>   r  r  r<   r<   r=   
_print_Str%  s    zPrettyPrinter._print_Str)N)F)T)N)N)r8  r9  )NNr   F)FNrZ   r[   )FNrP  FrZ   r[   )N)rs   
__module____qualname____doc__ZprintmethodZ_default_settingsr3   rB   propertyrD   rG   rJ   rK   rS   rU   Z_print_RandomSymbolrW   rY   rb   rh   rj   rk   rn   rp   ru   Z_print_InfinityZ_print_NegativeInfinityZ_print_EmptySetZ_print_NaturalsZ_print_Naturals0Z_print_IntegersZ_print_RationalsZ_print_ComplexesZ_print_EmptySequencerw   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r   r  r$  r7  r<  rA  rJ  rK  rM  rY  r^  ra  rb  rg  rl  rw  rz  r|  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r	  r  r  r  r   r#  r%  r&  r'  r  r*  r8  r;  r<  r?  rB  rE  rF  rG  rH  rI  rJ  rK  rM  rN  rO  rP  rQ  rW  r_  ra  rb  rc  rd  rf  rg  rh  rj  rk  rl  ro  rq  rr  ru  ry  r{  r|  r}  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Z_print_SeqPerZ_print_SeqAddZ_print_SeqMulrM   r  r  r  r  r   r  r  r  r  r
  r  r  r  r  r  r  r  r  r!  r#  r+  r-  r4  r5  r7  r=  r>  r?  rA  rB  rC  Z_print_bellrE  rF  rG  rI  rK  rM  rQ  rR  rU  rY  r[  r^  rb  rd  rg  rl  rn  rp  rq  rs  rw  ry  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r<   r<   r<   r=   r%      s  
					%%K6aE		

$f!# 8	0T 
  
%

		H=,			)
						r%   c                 K   s>   t |}|jd }t|}z|| W t| S t| 0 dS )zReturns a string containing the prettified form of expr.

    For information on keyword arguments see pretty_print function.

    r+   N)r%   r5   r    rG   )rA   r;   r  r+   Zuflagr<   r<   r=   r  )  s    

r  c                 K   s   t t| fi | dS )a  Prints expr in pretty form.

    pprint is just a shortcut for this function.

    Parameters
    ==========

    expr : expression
        The expression to print.

    wrap_line : bool, optional (default=True)
        Line wrapping enabled/disabled.

    num_columns : int or None, optional (default=None)
        Number of columns before line breaking (default to None which reads
        the terminal width), useful when using SymPy without terminal.

    use_unicode : bool or None, optional (default=None)
        Use unicode characters, such as the Greek letter pi instead of
        the string pi.

    full_prec : bool or string, optional (default="auto")
        Use full precision.

    order : bool or string, optional (default=None)
        Set to 'none' for long expressions if slow; default is None.

    use_unicode_sqrt_char : bool, optional (default=True)
        Use compact single-character square root symbol (when unambiguous).

    root_notation : bool, optional (default=True)
        Set to 'False' for printing exponents of the form 1/n in fractional form.
        By default exponent is printed in root form.

    mat_symbol_style : string, optional (default="plain")
        Set to "bold" for printing MatrixSymbols using a bold mathematical symbol face.
        By default the standard face is used.

    imaginary_unit : string, optional (default="i")
        Letter to use for imaginary unit when use_unicode is True.
        Can be "i" (default) or "j".
    N)printr  )rA   kwargsr<   r<   r=   pretty_print<  s    +r  c                 K   sH   ddl m} ddlm} d|vr(d|d< |t| fi ||  dS )a  Prints expr using the pager, in pretty form.

    This invokes a pager command using pydoc. Lines are not wrapped
    automatically. This routine is meant to be used with a pager that allows
    sideways scrolling, like ``less -S``.

    Parameters are the same as for ``pretty_print``. If you wish to wrap lines,
    pass ``num_columns=None`` to auto-detect the width of the terminal.

    r   )pager)getpreferredencodingr,   i  N)pydocr  localer  r  encode)rA   r;   r  r  r<   r<   r=   pager_printl  s
    r  );r  
sympy.corer   Zsympy.core.addr   sympy.core.containersr   sympy.core.functionr   Zsympy.core.mulr   sympy.core.numbersr   r	   sympy.core.powerr
   sympy.core.sortingr   sympy.core.symbolr   sympy.core.sympifyr   Zsympy.printing.conventionsr   Zsympy.printing.precedencer   r   r   Zsympy.printing.printerr   r   sympy.printing.strr   sympy.utilities.iterablesr   sympy.utilities.exceptionsr   Z sympy.printing.pretty.stringpictr   r   Z&sympy.printing.pretty.pretty_symbologyr   r   r   r   r   r   r    r!   r"   r#   r$   pprint_use_unicodepprint_try_use_unicoder%   r  r  pprintr  r<   r<   r<   r=   <module>   s`   4                      !
-