a \}}||}|D]$\}}| |||||qqdd| D} tj}t|t| D]}|| |<q4| S)aSolve a linear system of equations. Examples ======== Solve a linear system with a unique solution: >>> from sympy import symbols, Eq >>> from sympy.polys.matrices.linsolve import _linsolve >>> x, y = symbols('x, y') >>> eqs = [Eq(x + y, 1), Eq(x - y, 2)] >>> _linsolve(eqs, [x, y]) {x: 3/2, y: -1/2} In the case of underdetermined systems the solution will be expressed in terms of the unknown symbols that are unconstrained: >>> _linsolve([Eq(x + y, 0)], [x, y]) {x: -y, y: y} rNr cSsi|]\}}|t|qSr).0stermsrrm/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/polys/matrices/linsolve.py jz_linsolve..)len_linear_eq_to_dictsympy_dict_to_dmdomainZ is_RealFieldZis_ComplexFieldZto_ddmZrrefZto_sdmr r r ZonerlistitemsappendZto_sympyziprZeroset)eqssymsnsymseqsdictrhsZAaugKZArrefZpivotsZnzcolsPVZ nonpivotsZsolivZnpiZVisymZzerorrrr _linsolve.s.    r+c st|jdd|D}t|ddd\}}tt||t|}t|}tt|t|g}t||D]@\} } fdd| D} | r|  | |<| rh|| qht t |||df|} | S)z?Convert a system of dict equations to a sparse augmented matrixcss|]}|VqdSN)values)rerrr wrz#sympy_dict_to_dm..T)field extensioncsi|]\}}||qSrr)rrcZelem_mapZ sym2indexrrrrz$sympy_dict_to_dm..r ) runionrdictrrrangerrr enumerate) Z eqs_coeffseqs_rhsr!elemsr%Zelems_KZneqsr"r#eqr$eqdictZsdm_augrr3rrus rcsddfdd|DS)zUse expand to cancel nonlinear terms. This approach matches previous behaviour of linsolve but should be deprecated. cSs|jr|j|j}|Sr,) is_Equalitylhsr$expand)r:rrr expand_eqs z)_expand_eqs_deprecated..expand_eqcsg|] }|qSrr)rr:r?rr rz*_expand_eqs_deprecated..r)r rr@r_expand_eqs_deprecatedsrBcCs6z t||WSty0t|}t||YS0dS)1Convert a system Expr/Eq equations into dict formN)_linear_eq_to_dict_innerrrB)r r!rrrrs   rcCsFt|}gg}}|D]&}t||\}}||||q||fS)rC)r _lin_eq2dictr)r r!r#r8r:r$r;rrrrDs   rDc sX||vrtj|tjifS|jrtt}g}|jD]<}t||\}}||| D]\}}|||qTq0t |dd| D} | fS|j r"d} } g}|jD]8}t||\}}|s||q| dur|} |} qt qt || durifSfdd| D} | | fSn2|jr.Ncsi|]\}}||qSrr)rr*r2Zcoeffrrrr)rrZOneZis_AddrrargsrErrrZis_Mulrrr<r=r$Zhas_free) aZsymsetZ terms_listZ coeff_listZaiciZtiZmijZcijrZ terms_coeffrrFrrEsD      rEN) collectionsrZsympy.core.addrZsympy.core.mulrZsympy.core.singletonrZsympy.polys.constructorrZsympy.polys.solversrZsdmr r r r r+rrBrrDrErrrrs      G