z i0pSrSSKJr SSKrSSKJr SSKrSSKJr SSKJ r SSK r SSK J r "SS 5rg) z SpecialPolynomial class. ) annotationsN) combinations)reduce)mul) QiskitErrorcj\rSrSrSrSrSrSrSrSr Sr S r S r S r \S 5rS rSrSrg)SpecialPolynomialzdMultivariate polynomial with special form. Maximum degree 3, n Z_2 variables, coefficients in Z_8. cUS:a [S5eXl[XS- -S- 5Ul[XS- -US- -S- 5UlSUl[ R"U[ RS9Ul [ R"UR[ RS9Ul [ R"UR[ RS9Ul g)z2Construct the zero polynomial on n_vars variables.z*n_vars for SpecialPolynomial is too small.r)dtypeN) rn_varsintnc2nc3weight_0npzerosint8weight_1weight_2weight_3)selfrs k/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/quantum_info/operators/dihedral/polynomial.py__init__SpecialPolynomial.__init__!s A:JK K v!,q01v!, ;a?@ rww7 9 9 c[U5nUS:a [S5e[R"U5nUS:R 5(a,X0R :R 5(a [S5eUS:a7[R "U5S:*R 5(a [S5e[UR 5nUS:Xa[R"U5nU$//n[[[UR 5SS95n[[[UR 5SS95n[[[UR 5S S95nXV-U-U-Hfn URU 5n [[U 5R[U555n UR!XRU 5U -S -5 Mh U$) z?Multiply by a monomial given by indices. Returns the product. z-There is no term with on more than 3 indices.rIndices are out of bounds.r zIndices are non-increasing!rr )lenrrarrayanyrdiffr copydeepcopylistrrangeget_termsetunionset_term) rindiceslength indices_arrresultterms0terms1terms2terms3termvaluenew_terms r mul_monomialSpecialPolynomial.mul_monomial2sx W Q;MN Nhhw' !O " " kk(A'F'F'H'H:; ; A:277;/1499;;;< <"4;;/ Q;]]4(F TF,uT[['9Q?@F,uT[['9Q?@F,uT[['9Q?@F&069 d+D G =>??8+Du+LPQ*QR: rc<[U[5(d [U5n[UR5n[U[5(a^URU-S-UlUR U-S-UlUR U-S-UlURU-S-UlU$URUR:wa [S5e//n[[[UR5SS95n[[[UR5SS95n[[[UR5SS95nX4-U-U-HKnURU5nUS:wdM[R"U5n U RU5n X-n X)-nMM U$)zMultiply two polynomials.r&z#Multiplication on different n_vars.r r#r r%r) isinstancer rrrrrrrr-rr.r/r+r,r>) rotherr6r7r8r9r:r;r<temps r__mul__SpecialPolynomial.__mul__Ms`%!233JE"4;;/ eS ! !#}}u49FO#}}u49FO#}}u49FO#}}u49FO {{ell*!"GHHTF,uT[['9Q?@F,uT[['9Q?@F,uT[['9Q?@F&069t,A:==.D,,T2D >"4;;/==5>>9Q>==5>>9Q>==5>>9Q>==5>>9Q> rc [U5UR:wa [S5eUVs/sHn[U[5PM nnUVs/sHn[U[ 5PM nnSU;aSU;a [S5eSU;nU(d9SUVs/sHofRUR:HPM sn;a [S5eOUS-n//n[ [[UR5SS95n[ [[UR5SS95n [ [[UR5SS95n U(aS n Sn O1[ UR5n [ UR5n SU l Xx-U -U -HGn URU 5nUS :wdM[[U Vs/sHoUPM snU 5nXU--n MI [U [5(aU S -n U $s snfs snfs snfs snf) zEvaluate the multinomial at xval. if xval is a length n z2 vector, return element of Z8. if xval is a length n vector of multinomials, return a multinomial. The multinomials must all be on n vars. z&Evaluate on wrong number of variables.FzEvaluate on a wrong type.z%Evaluate on incompatible polynomials.r r r#r%rr&) r'rrrArr r-rr.rr/rr)rxvalx check_int check_polyis_intir7r8r9r:r6startr;r<jnewterms revaluateSpecialPolynomial.evaluate{s t9 #FG G156AZ3' 6@DE1j$56 E I %:"59: :i'$?$QT[[0$??!"IJJ@!8Dl5#5;<l5#5;<l5#5;< FE&t{{3F%dkk2EENOf,v5DMM$'Ez &=1Aw&=uE'/1 6 fc " "aZF ?7E @*'>sG) G. "G3,G8 c[R"U5nUS:R5(d!X R:R5(a [ S5e[ U5n[ R"US5n[ R"US5nSUl[R"UR5Ul [R"UR5Ul [R"UR5UlUHnURU/S5 M UHnUR[!U5S5 M UHnUR[!U5S5 M g) zoSet to special form polynomial on subset of variables. p_J(x) := sum_{a subseteq J,|a| neq 0} (-2)^{|a|-1}x^a rr"r r%r rr!N)rr(r)rrsorted itertoolsrrrrrrrrr2r-)rr3r5 subsets_2 subsets_3rTs rset_pjSpecialPolynomial.set_pjs hhw' !O " "{kk'A&F&F&H&H:; ;/**7A6 **7A6  - * * A MM1#q !A MM$q'1 %A MM$q'1 %rc[U5nUS:ag[R"U5nUS:R5(d!X0R:R5(a [ S5eUS:a7[R "U5S:*R5(a [ S5eUS:Xa UR$US:XaURUS$US:XaU[USUR-USS-US-S- - 5n[USUS- S- 5nURXE-$URUS- n[US- US- -US- -S- 5nURUS- n[US- US- -S- 5nURUS- n[URURS- -URS- -S- U- U- U- 5n URU $) aGet the value of a term given the list of variables. Example: indices = [] returns the constant indices = [0] returns the coefficient of x_0 indices = [0,3] returns the coefficient of x_0x_3 indices = [0,1,3] returns the coefficient of x_0x_1x_3 If len(indices) > 3 the method fails. If the indices are out of bounds the method fails. If the indices are not increasing the method fails. r!rr"r Indices are non-increasing.r r%r r'rr(r)rrr*rrrrr) rr3r4r5offset_1offset_2tmp_1tmp_2offset_3offsets rr/SpecialPolynomial.get_termsW Q;hhw' !O " "{kk'A&F&F&H&H:; ; A:277;/1499;;;< < Q;== Q;==, , Q;71: 3 Q'RS*7TXY6YYZH71: 2Q67H==!45 5 gaj( eai0EAI>BC gaj( eai0145;;+ KK4;;? +t{{Q ?! Ch NQY Y\d d }}V$$rc[U5nUS:ag[R"U5nUS:R5(d!X@R:R5(a [ S5eUS:a7[R "U5S:*R5(a [ S5eUS-nUS:XaX lgUS:XaX RUS'gUS:XaU[USUR-USS-US-S- - 5n[USUS- S- 5nX RXV-'gURUS- n[US - US- -US- -S - 5nURUS- n[US- US- -S- 5nURUS- n [URURS- -URS- -S - U- U- U - 5n X RU 'g) aSet the value of a term given the list of variables. Example: indices = [] returns the constant indices = [0] returns the coefficient of x_0 indices = [0,3] returns the coefficient of x_0x_3 indices = [0,1,3] returns the coefficient of x_0x_1x_3 If len(indices) > 3 the method fails. If the indices are out of bounds the method fails. If the indices are not increasing the method fails. The value is reduced modulo 8. r!Nrr"r r`r&r r%rra) rr3r<r4r5rbrcrdrerfrgs rr2SpecialPolynomial.set_termsW Q; hhw' !O " "{kk'A&F&F&H&H:; ; A:277;/1499;;;< <  Q;!M q[(-MM'!* % q[71: 3 Q'RS*7TXY6YYZH71: 2Q67H16MM(- .KK'!*,EEAI%!)4 BQFGHKK'!*,EEAI%!)4q89H{{WQZ/H t{{Q/4;;?CaGF %*MM& !rcUR[UR5[UR5[UR54nU$)zReturn a string representation.)rtuplerrr)rtups rkeySpecialPolynomial.keys9}}eDMM2E$--4H%PTP]P]J^_ rcb[U[5=(a URUR:H$)zTest equality.)rAr rn)rrNs r__eq__SpecialPolynomial.__eq__s"!./EDHH4EErc[UR5n[UR5HJnUR U/5nUS:wdMUS- nUS:waU[U5S-- nUS[U5-- nML [URS- 5Hyn[US-UR5HYnUR X$/5nUS:wdMUS- nUS:waU[U5S-- nUS[U5-S-[U5-- nM[ M{ [URS- 5Hn[US-URS- 5Hn[US-UR5HinUR X$U/5nUS:wdMUS- nUS:waU[U5S-- nUS[U5-S-[U5-S-[U5-- nMk M M U$)z'Return formatted string representation.rz + r *x_z*x_r )strrr.rr/)routrRr<rTks r__str__SpecialPolynomial.__str__s$-- t{{#AMM1#&Ezu A:3u:++Ctc!f}$ $t{{Q'A1q5$++. qf-A:5LCzs5zC//4#a&=503q699C /(t{{Q'A1q5$++/2q1udkk2A MM1)4Ezu  A:3u:#33Ctc!f}u4s1v=EANN 33( r)rrrrrrrN)__name__ __module__ __qualname____firstlineno____doc__rr>rDrGrJrVr]r/r2propertyrnrqry__static_attributes__rrr r sV :"64# (T&,)%V,*\ Frr )r __future__rrZrr+ functoolsroperatorrnumpyrqiskit.exceptionsrr rrrrs0#" )^^r