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5.6.1 Computation with Polynomials

118006 ^QAdd ( o1 → o2+o1 )
Adds two polynomials.
119006 ^RADDext ( o2 o1 → o2+o1 )
Internal +. This is the same entry as ^QAdd.
117006 ^SWAPRADD ( o2 o1 → o1+o2 )
SWAP, then QAdd.
115006 ^QSub ( o2 o1 → o2-o1 )
Subtracts two polynomials.
116006 ^RSUBext ( o2 o1 → o2-o1 )
Internal -. This is the same entry as ^QSub.
114006 ^SWAPRSUB ( o2 o1 → o1-o2 )
SWAP, then QSub.
111006 ^QMul ( Q1 Q2 → Q )
Multiplication of polynomials with extensions.
112006 ^RMULText ( Q1 Q2 → Q )
Multiplication of polynomials with extensions. This is the same entry as ^QMul.
110006 ^SWAPRMULT ( Q1 Q2 → Q )
SWAP, then ^QMul.
11C006 ^QDiv ( o2 o1 → o2/o1 )
Internal /.
11B006 ^RDIVext ( o2 o1 → o2/o1 )
Internal /. This is the same entry as ^QDiv.
11A006 ^SWAPRDIV ( o2 o1 → o1/o2 )
SWAP, then QDiv.
0D9006 ^QMod ( Q, Z → Q mod Z )
0DF006 ^QRoot
Extracts Nth power factors from polynomial.
113006 ^RASOP ( n1/d1 n2/d2 → d1*d2 n1*d2 n2*d1 )
Used by RADDext and RSUBext for rational input.
11D006 ^R15SIMP
11E006 ^PPow#
11F006 ^RP# ( o2 # → o2^# )
Internal power (not for matrices).
120006 ^MPext ( ob # prg* → ob^# )
General power with a specified multiplication program.
123006 ^RPext ( o2 o1 → o2^o1 )
Tries to convert o1 to an integer to call RP#, otherwise x^ext.
122006 ^MPEXEC
108006 ^DISTDIVext ( P Q → quo mod T )
( P Q → P Q F )
Euclidean division. Assumes P and Q have integer coefficientes. Returns FALSE if sparse short division fails.
3E5006 ^PTAYLext ( P, r → symb )
Taylor for polynomials.
15B006 ^CARCOMPext ( Q1/Q2 → Q1'/Q2' )
Extracts leading coefficients for the first variable from a rational polynomial.
3EE006 ^QDivRem ( ob2 ob1 → quo mod )
Polynomial Euclidean division of 2 objects. Dispatchs to DIV2LISText for list polynomials.
3EF006 ^DIV2LISText ( Z0 l1 l2 → div mod )
Euclidean division, l1 and l2 are list polynomials. Test first if l1=l2, then tries fast division, if it fails switch to SRPL division.
3F8006 ^PDIV2ext ( A B → Q R )
Step by step Euclidean division for univar poly.
3F9006 ^PSetSign ( P1 P2 → sign[P2]*P1 )
Sets sign of P1 according to leading coeff of P2.
3C4006 ^ModExpa ( Zn Fraction → Fraction modulo Zn )
3C5006 ^ModAdd ( Q1 Q2 Zn → Z )
Modular addition. Z = Q1+Q2 (mod Zn).
3C6006 ^ModSub ( Q1 Q2 Zn → Z )
Modular subtraction. Z = Q1-Q2 (mod Zn).
3C7006 ^ModMul ( Q1 Q2 Zn → Z )
Modular multiplication. Z = Q1*Q2 (mod Zn).
3C8006 ^ModDiv ( Z1 Z2 Zn → Z )
Modular division. Z = Z1/Z2 (mod Zn).
3C9006 ^ModDiv2 ( Q1 Q2 Zn → quo mod mod' )
Modular division. mod' = Q1 mod Q2 mod Zn. If Q1 and Q2 are integers, Q1 mod Q2 mod Zn is always 0.
3CA006 ^ModInv ( Z Zn → Z' )
Modular inversion. Z' = INV(Z) (mod Zn). NONINTERR if GCD[Z,Zn] ≠ 1 or if Z = 0 (otherwise the results would be unpredictable).
3CB006 ^ModGcd ( Q1 Q2 Zn → Q' )
Modular GCD.
3CC006 ^ModLGCD
3CD006 ^ModLOPD
3CE006 ^MODULOMODext
3CF006 ^MODULOMAText
3D1006 ^ModFctr


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