Looking for library to solve Inequation

[Anabelle06]

Hi i'm actually a student looking to solve inequation :
A+B < M1
A+C < M1

I can't find any library that's make me able to solve this. Could you please give me some clue about it?

Thanks very much in advance.

[Moschops]

When you say "solve", what do you mean? What is the "answer" you're looking for to the above posted two inequalities?

[ResidentBiscuit]

if(A+B < M1)?

OR...

if((A+B) - M1 < 0)

Not sure what you mean here

[soranz]

arn't these equivalent ?

if(A+B < M1)?

OR...

if((A+B) - M1 < 0)

[ResidentBiscuit]

arn't these equivalent ?

Yes, that's why I put them.

[soranz]

Given this problem:

A+B < M1
A+C < M1


Something looks off. multiplying the 2nd inequality by -1 we get:

A+B < M1
-A-C < -M1

Then adding them together we get:
B - C < 0 or B < C

Doing the same the other way around we get:
C < B

If both C < B and B < C then C must equal to B making this not an inequality or did I forget how to do math ? lol

[ResidentBiscuit]

A+B < A+C
B < C

and

A+C < A+B
C < B

That and should be an or I believe.

We don't know the relationship between B and C.

[soranz]

We don't know the relationship between B and C.

True, since the poster was not very specific.

Assuming this is meant to be a system of inequations with no constants they are related by A and M1 such that:

A+B < M1
A+C < M1

Plotting for all values that satisfy one inequation will be a complete union with the other inequation.

[viliml]

There are 3*infinity possible integer solutions:
a = n_1+n_2-n_3-n_4-n_5-n_6-n_7-1, b = -n_1+n_3+n_4+n_8+n_9-n_10-n_11, c = -n_1+n_4+n_5+n_9-n_10+n_12-n_13, m = n_2-n_7+n_8+n_9-n_10+n_12+n_14, n_1 element Z, n_1 >=0, n_2 element Z, n_2 >=0, n_3 element Z, n_3 >=0, n_4 element Z, n_4 >=0, n_5 element Z, n_5 >=0, n_6 element Z, n_6 >=0, n_7 element Z, n_7 >=0, n_8 element Z, n_8 >=0, n_9 element Z, n_9 >=0, n_10 element Z, n_10 >=0, n_11 element Z, n_11 >=0, n_12 element Z, n_12 >=0, n_13 element Z, n_13 >=0, n_14 element Z, n_14 >=0,

a = n_1+n_2-n_3-n_4-n_5-n_6-n_7, b = -n_1+n_3+n_4+n_8+n_9-n_10-n_11-1, c = -n_1+n_4+n_5+n_9-n_10+n_12-n_13-1, m = n_2-n_7+n_8+n_9-n_10+n_12+n_14, n_1 element Z, n_1 >=0, n_2 element Z, n_2 >=0, n_3 element Z, n_3 >=0, n_4 element Z, n_4 >=0, n_5 element Z, n_5 >=0, n_6 element Z, n_6 >=0, n_7 element Z, n_7 >=0, n_8 element Z, n_8 >=0, n_9 element Z, n_9 >=0, n_10 element Z, n_10 >=0, n_11 element Z, n_11 >=0, n_12 element Z, n_12 >=0, n_13 element Z, n_13 >=0, n_14 element Z, n_14 >=0, and

a = n_1+n_2-n_3-n_4-n_5-n_6-n_7, b = -n_1+n_3+n_4+n_8+n_9-n_10-n_11, c = -n_1+n_4+n_5+n_9-n_10+n_12-n_13, m = n_2-n_7+n_8+n_9-n_10+n_12+n_14+1, n_1 element Z, n_1 >=0, n_2 element Z, n_2 >=0, n_3 element Z, n_3 >=0, n_4 element Z, n_4 >=0, n_5 element Z, n_5 >=0, n_6 element Z, n_6 >=0, n_7 element Z, n_7 >=0, n_8 element Z, n_8 >=0, n_9 element Z, n_9 >=0, n_10 element Z, n_10 >=0, n_11 element Z, n_11 >=0, n_12 element Z, n_12 >=0, n_13 element Z, n_13 >=0, n_14 element Z, n_14 >=0.
I copied that from WolframAlpha.

[Veltas]

Everyone (EDIT: Soranz) please stop making up your own algebra. XD

If we're told:
A+B < M1
A+C < M1

then we basically know nothing.

Soranz, you may be interested to know that multiplying by a negative number changes the direction of the inequality sign, and multiplying by 0 makes it an equals sign.

Simply adding the equations together will only lose us information from the two inequalities, and garners:
2 A + B + C < 2 M1

Which is true, but less specific than the original set of equations and therefore less helpful.

Algebra isn't magic, if you're given no real information to work with it can't generate magic answers, unfortunately.

[soranz]

I am thanks!!! Google wasn't my friend yesterday when trying to find out info on inequalities XD