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RegularChains[FastArithmeticTools]

  

RandomRegularChainDim1

  

generate a random one-dim regular chain

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

RandomRegularChainDim1(lv, ld, p)

Parameters

lv

-

a list of variables

ld

-

a list of degrees

p

-

a prime number

Description

• 

The command RandomRegularChainDim1 returns a randomly generated one-dimensional regular chain with lv as variables. The degree sequence of the variables is ld. All the coefficients of the polynomials are reduced w.r.t p.

Examples

withRegularChains:

withChainTools:

withFastArithmeticTools:

p962592769:

varsx1,x2,x3,x4:

RPolynomialRingvars,p:

Randomly generating (dense) regular chain and polynomial

Nnopsvars:

dg3:

degsseq2,i=1..N:

bound35:

polrandpolyvars,dense,degree=dg+randmodpmodp:

tcRandomRegularChainDim1vars,degs,p

tc:=regular_chain

(1)

Computing with the modpn-supported and modular code

r1IteratedResultantDim1pol,tc,R,x4,bound

r1:=941032609x424+942118408x423+194753142x422+341712954x421+2338033x420+475384741x419+457989148x418+681536348x417+718107114x416+148212901x415+33032177x414+214227263x413+150959749x412+8508997x411+76347793x410+927296123x49+733361705x48+689644959x47+204369026x46+361192708x45+138352162x44+832291904x43+263580044x42+106333828x4+323296554

(2)

Computing with the non-fast non-modular code

r2IteratedResultantpol,tc,R

r2:=941032609x424+942118408x423+194753142x422+341712954x421+2338033x420+475384741x419+457989148x418+681536348x417+718107114x416+148212901x415+33032177x414+214227263x413+150959749x412+8508997x411+76347793x410+927296123x49+733361705x48+689644959x47+204369026x46+361192708x45+138352162x44+832291904x43+263580044x42+106333828x4+323296554

(3)

The results computed by IteratedResultantDim1 and IteratedResultant are equivalent.

evalbr1=r2

true

(4)

See Also

IteratedResultant

IteratedResultantDim0

IteratedResultantDim1

RandomRegularChainDim0

RegularChains

 


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