09B006 |
^ONE{}POLY
|
( ob → {ob} ob1 → Q )
Replaces ONE{}N for polynomial
building.
|
09C006 |
^TWO{}POLY
|
( ob1 ob2 → Q )
Replaces TWO{}N for polynomial
building.
|
09D006 |
^THREE{}POLY
|
( ob1 ob2 ob3 → Q )
Replaces THREE{}N for polynomial
building.
|
09E006 |
^TWO::POLY
|
( ob1 ob2 → :: )
Replaces 2Ob>Seco for polynomial
building.
|
09F006 |
^::POLY
|
( Meta → :: )
Replaces ::N for polynomial building.
As opposed to the regular ::N code, we do pop
the binary number. This is enforced by the
entry to the common polyxml code.
|
0A0006 |
^{}POLY
|
( Meta → Q )
Replaces {}N for polynomial building.
As opposed to the regular {}N code, we do pop
the binary number. This allows us to enter
the code here with fixed sizes, as in
ONE{}POLY and TWO{}POLY.
|
0A7006 |
^>POLY
|
( Meta → Q )
Builds polynomial.
|
0A1006 |
^>TPOLY
|
( P ob → P' )
Replaces >TCOMP for polynomial
building.
|
0A2006 |
^>HPOLY
|
( P ob → P' )
Replaces >HCOMP for polynomial
building.
|
0A3006 |
^>TPOLYN
|
( P ob1 .. obn #n → P' )
Improved >TCOMP for polynomial building.
|
0A4006 |
^>HPOLYN
|
( P ob1 .. obn #n → P' )
Improved >HCOMP for polynomial building.
|
0A5006 |
^MKPOLY
|
( #n #k → P )
Makes polynomial of nth variable to the power
k.
|
2AB006 |
^MAKEPROFOND
|
( ob # → {{{...{o}...}}} )
Embedds ob in the given number of lists.
|
4F4006 |
^TRIMext
|
( Q → Q' )
Removes unnecessary zeros from polynomial.
|
4F5006 |
^PTrim
|
( ob → ob' )
Trims polynomial.
|
0A6006 |
^ONE>POLY
|
( Q → Q' )
Increases variable depth. Constants (Z,Irr,C)
are not modified.
|
302006 |
^TCHEBext
|
( zint → P )
Tchebycheff polynomial. If zint>0 then 1st
kind, if <0 then second kind.
|
3DE006 |
^LRDMext
|
( P # → [] )
Left ReDiMension. Adds 0 to the left of
polynomial to get a symbolic vector of lenght
#+1.
|
3DF006 |
^RRDMext
|
( {} # → {} )
Right ReDiMension: like <REF>LRDMext but 0 at
the right and {}.
|
3E0006 |
^DEGREext
|
( {} → degre )
Degree of a list-polynomial.
|
3E1006 |
^FHORNER
|
( P/d r → P[X]_div_[X-r]/d r P[r]/d )
Horner scheme.
|
3E2006 |
^HORNext
|
( P r → P[X]_div_[X-r] r P[r] )
Horner scheme.
|
3E3006 |
^HORN1
|
|
3E4006 |
^MHORNext
|
( P r → P[X]_div_[X-r] r P[r] )
Horner scheme for matrices.
|
3E6006 |
^LAGRANGEext
|
( M → symb )
Lagrange interpolation. Format of the matrix
is
[ [ x1 .. xn ] [ f(x1) .. f(xn) ] ]
Returns a polynomial P such that P(xi)=f(xi)
|
10F007 |
^RESULTANT
|
( P1 P2 → P )
Resultant of two polynomials. Depth of P is
one less than depth of P1 and P2.
First available in ROM 1.11.
|
110007 |
^RESULTANTLP
|
( res g h P1 P2 → +/-res g' h' P1' P2' )
Subresultant algorithm innerloop.
First available in ROM 1.11.
|
111007 |
^RESPSHIFTQ
|
( P Q → P' )
Resultant of P and Q shifted.
gcd[Q(x-r),P(x)]!=1 equivalent to r root of
P' P' has same depth than P and Q.
First available in ROM 1.11.
|
112007 |
^ADDONEVAR
|
( P → P' )
Adds one variable just below the main var.
works for polynomial, not for fractions.
First available in ROM 1.11.
|
0CF007 |
^SHRINKEVEN
|
( P → P' )
Changes var Y=X^2 in an even polynomial.
|
0D0007 |
^SINTEST
|
|
0D1007 |
^SHRINK2SYM
|
( N D → N' D' )
Shrinks 2 polynomials using symmetry
properties.
|
0D2007 |
^SHRINKSYM
|
( N → N' )
Shrinks 1 polynomial using symmetry
properties. Degree of N must be even. If it
is odd then N should be divided by X+1.
|
0D3007 |
^SHRINK2ASYM
|
( N D → N' D' )
Shrinks 2 polynomials using antisymmetry
properties.
|
0D4007 |
^SHRINKASYM
|
( N → N' )
Shrinks 1 polynomial using antisymmetry
properties. Degree of N must be even. If it
is odd then N should be divided by X+1.
|
103006 |
^PNMax
|
( P → Z )
Gets the coefficient of P with max norm.
|
161006 |
^SWAPNDXF
|
( Qden Qnom → symb )
Builds a symbolic from rational polynomial.
|
162006 |
^NDXFext
|
( Qnom Qden → symb )
Builds a symbolic from rational polynomial.
|
163006 |
^SWAPFXND
|
( symb ob → ob Qnom Qden )
Converts symbolic to rational polynomial.
|
164006 |
^FXNDext
|
( symb → Qnom Qden )
Converts symbolic to rational polynomial.
|
3D7006 |
^REGCDext
|
( a b → d u v au+bv=d )
|
3D8006 |
^EGCDext
|
( a b → d u v au+bv=d )
Bezout identity for polynomials.
|
0EA006 |
^PEvalFast?
|
( Z Pn → Z Pn F / Pn[Z] T )
Attempts to evaluate Pn at X1=Z using fast
register arithmetic.
Fails if any of the following is true:
Pn is not sunivariate;
Z is polynomial after all;
Z size is too big for register;
Any overflow occurs during Horner evaluation.
|
10E007 |
^FLAGRESULTANT
|
( symb1 symb2 → symb )
Resultant of two polynomials in symbolic
form.
First available in ROM 1.11.
|