|Bill Allombert on Wed, 04 Sep 2013 13:37:44 +0200|
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|Re: solve system of linear equations mod p - more than one solution|
On Tue, Sep 03, 2013 at 08:40:19AM -0400, Mark DeBonis wrote: > Is PARI able to solve a system of linear equations modulo p which have more > than one solution? (there are free variables) Can it list the complete > solution set in some manner? Can you choose which variables to solve for? Yes, use matinverseimage and matker. For example: ? p=101;A=[1,2,3;4,5,6]*Mod(1,p);B=[7,8]~*Mod(1,p); ? S=matinverseimage(A,B) %11 = [Mod(61,101),Mod(74,101),Mod(0,101)]~ ? K=matker(A) %12 = [Mod(1,101);Mod(99,101);Mod(1,101)] ? S+K*[lambda]~ %13 = [Mod(1,101)*lambda+Mod(61,101),Mod(99,101)*lambda+Mod(74,101),Mod(1,101)*lambda]~ Cheers, Bill.