272006 |
^MULMULText
|
( {} % → {}' )
Multiplies multiplicities in a factor list by
coeff.
|
273006 |
^METAMULMULT
|
|
274006 |
^METAMM2
|
( meta % → meta' )
Multiplies by % all multiplicities of meta.
|
275006 |
^COMPLISText
|
( {} → {}' )
|
276006 |
^METACOMPRIM
|
( Meta → Meta' )
Suppresses multiple occurrances of the same
factor by adding corresponding
multiplicities.
|
277006 |
^METACOMP0
|
|
278006 |
^METACOMP1
|
( f1...fk-1 mk-1 meta-res mk fk # → f1...fk-1 mk-1 meta-res )
|
279006 |
^ADDLISText
|
( {} %n ob → {}' )
Adds ob with multiplicity %n to the
list. Checks if ob is in {}.
|
27A006 |
^DIVISext
|
( ob → {divisors} )
Returns list of divisors of ob.
|
27B006 |
^FACT1ext
|
( symb-poly → Lvar Q {} )
{} is the list of root/multiplicity of sym
with respect to the current variable.
|
27C006 |
^FACTOext
|
( symb → Lvar Q {} )
{} is the list of factors/multiplicity of
symb.
|
27D006 |
^ZFACTO
|
( C → {} C Lfact )
|
27E006 |
^SOLVext
|
( symb → {} )
Numeric solver for univariate polynomials.
The list contains the roots without
multiplicity.
|
27F006 |
^FRND
|
( ob → ob') )
Float rounding for %%, C%% or list of either
type. Used by SOLVext to reconstruct
factors.
|
280006 |
^BICARREE?
|
( P #5 → meta cst_coeff T )
( P #5 → P #5 F )
( P # → P # F )
Searches if P is a bisquared 4-th order
equation. Returns a meta of factors and the
multiplying coeff in that case.
|
281006 |
^REALBICAR
|
( f1 #1 coef → meta rest T )
|
113007 |
^IROOTS
|
( P → list )
Finds integer roots of a polynomial.
First available in ROM 1.11.
|
283006 |
^EVIDENText
|
( P → meta cst_coeff )
Returns the roots of a polynomial P.
Calls the numeric solver.
|
284006 |
^EVIDSOLV
|
( P → meta cst_coeff )
Returns the roots of a 1st, 2nd order and some
other poly. Calls the numeric solver if
exact solving fails.
|
285006 |
^DEG2ext
|
( P → {} )
Returns the roots of a 2nd order polynomial.
|
286006 |
^METADEG2
|
( P → P meta )
Returns the roots of a 2nd order polynomial.
P must be of order 1 or 2.
|
287006 |
^METADEG1
|
( P → P meta )
Returns the roots of a 1st order polynomial.
P must be of order 1.
|
288006 |
^DEG1
|
( f → r )
Root of a first order factor.
f is one level depth deeper than r.
|
289006 |
^FDEG2ext
|
( P → meta-fact cst_coef )
Returns factors of a 2nd order polynomial and
the corresponding multiplying coefficient.
tests for 1st order polynomial.
|
28B006 |
^RACTOFACext
|
( r → n d )
Converts root to factor.
Factor is n/d, one level depth deeper than r.
|
28C006 |
^FACTORACext
|
( f → r cst_coef )
Converts a factor to a root, solving 1st order
factor. f and cst_coef are one level depth
deeper than r.
|
28D006 |
^RFACText
|
( ob # → {} intob meta )
{} is the list of variables. Meta is made of
roots or factors of numerator (N) or
denomenator (D) or both (N/D), depending on #.
ZERO for roots N/D; ONE for roots N;
TWO for roots D with numeric solver call;
THREE for roots D without num. solver call;
FOUR for factors N/D;
FIVE for factors N;
SIX for factors D with numeric solver call;
SEVEN for factors D without num.solver call.
|
28E006 |
^RFACT2ext
|
( ob {} # → {} intob meta )
Like <REF>RFACText, but the list of variables
is given.
|
28F006 |
^RFACTSTEP3
|
( ob → meta-fact )
Partial square-free factorization w.r.t. the
main variable. Extract trivial factors Etape
3 ob → meta-fact.
|
290006 |
^RFACTSTEP5
|
( %m on → add-to-meta-res )
Factorization of a square-free polynomial.
|
291006 |
^METASOLV
|
( pn cst_coeff → meta cst_coeff )
Non-integer factorization (sqrt extensions
and numeric). multiplicty is in LAM 5,.
|
292006 |
^METASOLVOUT
|
|
293006 |
^METASOLV2
|
( cst_coeff p → fr1 %m [fr2 %m] # cst_coeff )
Returns roots/factors of 1st and 2nd order
polynomials.
|
294006 |
^METASOLV4
|
( cst1 f1 ... fk #k cst2 → fr1 %m ... frn %m #2k cst_coeff )
Returns factors or convert to roots if
needed.
#k=1,2 or 4, fk are of order 1 or 2.
|
295006 |
^ADDMULTIPL
|
( meta cst_coeff → meta' cst_coeff )
Adds multiplicities to a meta.
Multiplicity is in LAM 5.
|
296006 |
^FACTOOBJext
|
( { fact mult } flag prg* prg^ → ob )
Rebuilds an object from its list of factors
(flag=TRUE) or roots (flag=FALSE) using prg*
to multiply and prg^ to take multiplicity
power.
|
29C006 |
^ID>DERext
|
( id → {} stripped_id )
|
093006 |
^ALG48MSOLV
|
( Lp → Lidnt Lsol )
Calculates Groebner basis multivar solution.
LAM3 must be bound to Lvar and LAM4 to Lidnt.
|
094006 |
^GMSOLV
|
( Lp → meta-sol )
Calculates Groebner basis multivar solutions.
LAM1 must be bound to the number of vars
A solution is a list { o1 ... on } where
#n=LAM1
ok embedded in k-1 lists is the value of the
k-th var ok may be undef.
|
095006 |
^GBASIS
|
( Lp → G )
Calculate Groebner basis.
G = { 1 } if no solutions
G = { 0 } if identically true.
|
096006 |
^GSOLVE
|
( Lp → Lg )
Calculate factorized Groebner basis.
Lg = { Lg1 Lg2 .. Lgn }
Lgi = independent solution (probably)
Lg = {} if no solutions
Lg = { { 0 } } if identically true.
|
097006 |
^GFACTOR
|
( Lp fctr? → Lg )
Calculate Groebner basis or factorized Groebner
basis. Redundant bases are not removed.
|
098006 |
^GREDUCE
|
Interreduce basis. Lambda variables
{{ fctr? G k tmp todo Lg Irred }}.
|
099006 |
^REDUCE
|
( p G → q )
Reduces polynomial with respect to given
basis.
|
09A006 |
^FASTREDUCE
|
( r P → q T / r P F )
Assembly version of REDUCE for polynomials
with short coefficients. Returns FALSE if an
overflow occurs during the reduction.
Assumes r is a genuine polynomial (not
constant). Assumes G is not empty. Assumes
G does not contain zeros (is trimmed).
|
37D006 |
^ROOTM2ROOT
|
( {}/V → V' )
Transforms list of root/multiplicites to
vector of roots.
|
0F2007 |
^PASCAL_NEXTLINE
|
( {} → {}' )
Finds next line in the Pascal triangle.
|
0F3007 |
^DELTAPSOLVE
|
( Q → P )
Solves P(x+1)-P(x)=Q(x).
Internal polynomial function.
|