becejac

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These are replies submitted by becejac

@mmcdara 

If A inter B is an empty set then all the elements from A have to multiply with elements in B like

{x1,x2,x3} and {x4, x5} then the solution is x1x4, x2x4, x3x4, x2x4, x2x5, x3x4 and x3x5

@mmcdara 

Is it possible to create undirected graph? I suppose in this line something has to be changed and be {1,2}, {1,3} etc instead of [1,2],[1,3] 

edges := { convert(M, listlist)[] }

{[1, 2], [1, 3], [2, 1], [2, 4], [2, 5], [3, 2], [4, 5], [5, 1], [5, 4]}

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@mmcdara 

 

Thank you very much! It works! :))))

@Carl Love 

I tried to do this in workshit "try2" which I posted above, but unsuccessfully :(

@Carl Love 

 

Here is the input form. Thank you in advance!

 

try2.mw

@Carl Love 

Thank you very much!!

@Carl Love 

Thank you very much!

Do you know what to do because when I enter your text, Maple says:

Error, invalid input: mul expects 2 arguments, but received 1
 

@Markiyan Hirnyk 

Thank you for your answer very much. I have troubles to solve this system in Maple because of slack variables. I know that one of the possible solution is x1=1, x7=1, x9=1, x10=1, x12=1, x18=1, x24=1, x25=1, x27=1 and x28=1, remaining x are all zeros. I don't know how to solve it now. In example 3 in paper you proposed, one equations has only one variable and in this system I don't have that. 
PS. I made a mistake in system, equation starting with x6: at the end it has to be 1 instead of 11, and equation starting with x12+x4+x13+... has to be x12+x15+x13+...

Thank you in advance!

@Kitonum 

Here is the system of inequalities I have to solve, but with Groebner Bases:

The first 30 are inequalities, and the last 30, form is x^2-x, are equalities, becasue all the solutions have to be binary.

I realy don't know how to solve this.


 

B30 := [x1+x2+x3 >= 1, x2+x1+x4+x5+x6 >= 1, x3+x1+x4 >= 1, x4+x3+x2+x6+x12 >= 1, x5+x2+x7 >= 1, x6+x2+x4+x7+x9+x10+x8+x28 >= 1, x7+x5+x6 >= 1, x8+x6+x28 >= 1, x9+x6+x10+x11 >= 1, x10+x6+x9+x17+x20+x21+x22 >= 1, x11+x9 >= 1, x12+x4+x13+x14+x4+x16 >= 1, x13+x12 >= 1, x14+x12+x15 >= 1, x15+x12+x14+x18+x23 >= 1, x16+x17+x12 >= 1, x17+x16+x10 >= 1, x18+x15+x19 >= 1, x19+x18+x20 >= 1, x20+x19+x10 >= 1, x21+x10+x22 >= 1, x22+x10+x21+x24 >= 1, x23+x24+x15 >= 1, x24+x23+x25+x22 >= 1, x25+x24+x26+x27 >= 1, x26+x25 >= 1, x27+x29+x30+x25+x28 >= 1, x28+x8+x6+x27 >= 1, x27+x29+x30 >= 1, x27+x29+x30 >= 1, x1^2-x1, x2^2-x2, x3^2-x3, x4^2-x4, x5^2-x5, x6^2-x6, x7^2-x7, x8^2-x8, x9^2-x9, x10^2-x10, x11^2-x11, x12^2-x12, x13^2-x13, x14^2-x14, x15^2-x15, x16^2-x16, x17^2-x17, x18^2-x18, x19^2-x19, x20^2-x20, x21^2-x21, x22^2-x22, x23^2-x23, x24^2-x24, x25^2-x25, x26^2-x26, x27^2-x27, x28^2-x28, x29^2-x29, x30^2-x30]

[1 <= x1+x2+x3, 1 <= x2+x1+x4+x5+x6, 1 <= x3+x1+x4, 1 <= x4+x3+x2+x6+x12, 1 <= x5+x2+x7, 1 <= x6+x2+x4+x7+x9+x10+x8+x28, 1 <= x7+x5+x6, 1 <= x8+x6+x28, 1 <= x9+x6+x10+x11, 1 <= x10+x6+x9+x17+x20+x21+x22, 1 <= x11+x9, 1 <= x12+2*x4+x13+x14+x16, 1 <= x13+x12, 1 <= x14+x12+x15, 1 <= x15+x12+x14+x18+x23, 1 <= x16+x17+x12, 1 <= x17+x16+x10, 1 <= x18+x15+x19, 1 <= x19+x18+x20, 1 <= x20+x19+x10, 1 <= x21+x10+x22, 1 <= x22+x10+x21+x24, 1 <= x23+x24+x15, 1 <= x24+x23+x25+x22, 1 <= x25+x24+x26+x27, 1 <= x26+x25, 1 <= x27+x29+x30+x25+x28, 1 <= x28+x8+x6+x27, 1 <= x27+x29+x30, 1 <= x27+x29+x30, x1^2-x1, x2^2-x2, x3^2-x3, x4^2-x4, x5^2-x5, x6^2-x6, x7^2-x7, x8^2-x8, x9^2-x9, x10^2-x10, x11^2-x11, x12^2-x12, x13^2-x13, x14^2-x14, x15^2-x15, x16^2-x16, x17^2-x17, x18^2-x18, x19^2-x19, x20^2-x20, x21^2-x21, x22^2-x22, x23^2-x23, x24^2-x24, x25^2-x25, x26^2-x26, x27^2-x27, x28^2-x28, x29^2-x29, x30^2-x30]

(1)

G1 := Groebner[Basis](B30, plex(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30))

Error, (in Groebner:-Basis) the first argument must be a list or set of polynomials or a PolynomialIdeal

 

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