Machine mathematical reasoning by clever substitutions, How to do with AI
I have three equations that relates five variables a, b, c, r, s with a sum and two ratios.
Eq. 1: a = b + c;
Eq. 2: s = b / a;
Eq. 3: r = b / c.
Given two values for any of the five variables I get a solution. But, this is not the automation problem I want to solve.
I can have the solution of variable r by simply knowing s. This is solved by a "human algorithm" as follows.
- Substitute a of Eq. 1 in Eq. 2.
- Divide the second term of the new Eq. 2 by the variable c.
- Replace b/c by the expression of Eq. 3.
That means s = r / (r+1).
The questions is -How can an AI algorithm solve this?, i.e. the machine should recognize that given the variable r she can obtain directly the variable s and do no require another variable.
artificial-intelligence symbolic-math
asked Nov 14 '18 at 15:45
LudgerSBLudgerSB
11
add a comment |
I have three equations that relates five variables a, b, c, r, s with a sum and two ratios.
Eq. 1: a = b + c;
Eq. 2: s = b / a;
Eq. 3: r = b / c.
Given two values for any of the five variables I get a solution. But, this is not the automation problem I want to solve.
I can have the solution of variable r by simply knowing s. This is solved by a "human algorithm" as follows.
- Substitute a of Eq. 1 in Eq. 2.
- Divide the second term of the new Eq. 2 by the variable c.
- Replace b/c by the expression of Eq. 3.
That means s = r / (r+1).
The questions is -How can an AI algorithm solve this?, i.e. the machine should recognize that given the variable r she can obtain directly the variable s and do no require another variable.
artificial-intelligence symbolic-math
asked Nov 14 '18 at 15:45
LudgerSBLudgerSB
11
add a comment |
I have three equations that relates five variables a, b, c, r, s with a sum and two ratios.
Eq. 1: a = b + c;
Eq. 2: s = b / a;
Eq. 3: r = b / c.
Given two values for any of the five variables I get a solution. But, this is not the automation problem I want to solve.
I can have the solution of variable r by simply knowing s. This is solved by a "human algorithm" as follows.
- Substitute a of Eq. 1 in Eq. 2.
- Divide the second term of the new Eq. 2 by the variable c.
- Replace b/c by the expression of Eq. 3.
That means s = r / (r+1).
The questions is -How can an AI algorithm solve this?, i.e. the machine should recognize that given the variable r she can obtain directly the variable s and do no require another variable.
artificial-intelligence symbolic-math
asked Nov 14 '18 at 15:45
LudgerSBLudgerSB
11
I have three equations that relates five variables a, b, c, r, s with a sum and two ratios.
Eq. 1: a = b + c;
Eq. 2: s = b / a;
Eq. 3: r = b / c.
Given two values for any of the five variables I get a solution. But, this is not the automation problem I want to solve.
I can have the solution of variable r by simply knowing s. This is solved by a "human algorithm" as follows.
- Substitute a of Eq. 1 in Eq. 2.
- Divide the second term of the new Eq. 2 by the variable c.
- Replace b/c by the expression of Eq. 3.
That means s = r / (r+1).
The questions is -How can an AI algorithm solve this?, i.e. the machine should recognize that given the variable r she can obtain directly the variable s and do no require another variable.
artificial-intelligence symbolic-math
artificial-intelligence symbolic-math
asked Nov 14 '18 at 15:45
LudgerSBLudgerSB
11
asked Nov 14 '18 at 15:45
LudgerSBLudgerSB
11
asked Nov 14 '18 at 15:45
LudgerSBLudgerSB
11
asked Nov 14 '18 at 15:45
LudgerSBLudgerSB
11
asked Nov 14 '18 at 15:45
LudgerSBLudgerSB
11
11
add a comment |
add a comment |
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