http://www.mapleprimes.com/posts/40824-Solutions-To-Under-And-Overdetermined-Systems en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Wed, 10 Jun 2026 17:03:37 GMT Wed, 10 Jun 2026 17:03:37 GMT The latest comments added to the Post, solutions to under- and over-determined systems http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/posts/40824-Solutions-To-Under-And-Overdetermined-Systems http://www.mapleprimes.com/posts/40824-Solutions-To-Under-And-Overdetermined-Systems?ref=Feed:MaplePrimes:solutions to under- and over-determined systems:Comments#comment75596 Shawn, If, as in your example, the equations are linear then you can use the theory of linear algebra to get an answer to your question. Here's one way that this could be done: <pre> with( LinearAlgebra ): EQS := { x + y = a, x - y = b, 2*x + 2*y = c }; A,b := GenerateMatrix( EQS, [x,y] ); M := &lt; A | b >; GaussianElimination( M ); </pre> Now, if each row has a pivot entry, then the system is consistent for every right-hand side. If there is a row that does not have a pivot entry, then the RHS must be zero for the system to be consistent. Setting these elements of the RHS to zero gives the constraints that must be satisfied in order for the system to be consistent. Depending on the specific form of your equations, you can get fancier. Does this help you to answer your question? Doug <pre> --------------------------------------------------------------------- Douglas B. Meade Math, USC, Columbia, SC 29208 E-mail: mailto:meade@math.sc.edu Phone: (803) 777-6183 URL: http://www.math.sc.edu/~meade/ </pre> The latest comments added to the Post, solutions to under- and over-determined systems 75596 Wed, 19 Sep 2007 22:33:27 Z Doug Meade Doug Meade http://www.mapleprimes.com/posts/40824-Solutions-To-Under-And-Overdetermined-Systems?ref=Feed:MaplePrimes:solutions to under- and over-determined systems:Comments#comment75593 Greetings Doug. Using your code as posted, since you are declaring b as a variable in the original equation, you cannot use it again in your assignment to GenerateMatrix. Maple complains as follows: Error, recursive assignment Changing the lower case b to something else (I used upper case), gives the proper result. >restart: >with( LinearAlgebra ): >EQS := { x + y = a, x - y = b, 2*x + 2*y = c }; >A,B := GenerateMatrix( EQS, [x,y] ); >M := < A | B >; >GaussianElimination( M ); Regards, Georgios Kokovidis Dräger Medical The latest comments added to the Post, solutions to under- and over-determined systems 75593 Thu, 20 Sep 2007 02:19:36 Z gkokovidis gkokovidis http://www.mapleprimes.com/posts/40824-Solutions-To-Under-And-Overdetermined-Systems?ref=Feed:MaplePrimes:solutions to under- and over-determined systems:Comments#comment75592 In solving a system such as this, you want to be careful about what is considered to be a variable and what is a parameter. Maple will give you solutions expressing a set of basic variables in terms of the other variables and the parameters; these will be valid for "generic" values of the parameters, but perhaps not for special values of the parameters. Thus: <pre> > sys := {x + y = a, x - y = b, 2*x + 2*y = c}: > solve(sys, {x,y}); </pre> This is treating x and y as the variables and a,b,c as parameters. It returns nothing since for generic values of parameters a, b and c, there are no solutions. But <pre> > solve(sys, {x,y,c}); </pre> Now x,y and c are considered as variables, so you pick up the solutions that depend on c having a specific relation to a and b: <maple>{c = 2*a, y = 1/2*a-1/2*b, x = 1/2*a+1/2*b}</maple> You might also try Groebner[Solve]: <pre> > Groebner[Solve](map(rhs-lhs,sys),[x,y,a,b,c]); </pre> Note that in the second argument, I list the variables first and then the parameters. <maple> {[[2*a-c, 4*y-c+2*b, -c-2*b+4*x], plex(x,y,a,b,c), {}]}</maple> The first item in the returned list indicates that in order to have a solution, you need <maple>2*a-c=0</maple>. Here's a system where the parameters enter the coefficients of x and y as well as the right sides: <pre> > sys2:= { a*x + y = b, b*x + y = c, x - y = a }: > G:= Groebner[Solve](map(rhs-lhs,sys2),[x,y,a,b,c]); </pre> <maple>G:={[[-b*a+c+a^2-b+a*c-b^2, b*a+b*y-c+y, y+y*a+b*a-c-a*c+b^2, -a+x-y], plex(x,y,a,b,c), {}]}</maple> Again, the first item in the list shows a condition on a,b,c that is needed in order to have a solution. The latest comments added to the Post, solutions to under- and over-determined systems 75592 Thu, 20 Sep 2007 03:04:27 Z Robert Israel Robert Israel http://www.mapleprimes.com/posts/40824-Solutions-To-Under-And-Overdetermined-Systems?ref=Feed:MaplePrimes:solutions to under- and over-determined systems:Comments#comment75579 Thanks everyone for your responses. My systems, unfortunately, are not linear and I'm not certain ahead of time which of the parameters (a,b,c in the example I gave), if any, may require a constraint. With this in mind, it looks like the Groebner approach is most promising. Thanks, Shawn The latest comments added to the Post, solutions to under- and over-determined systems 75579 Fri, 21 Sep 2007 03:01:28 Z Shawn Bauldry Shawn Bauldry