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Minimize beats Solve

Frank Kampas

Frank Kampas, Physicist at Large Consulting

Posted 2 years ago

This is the second step in solving a problem Reygan Dionisio posted on LinkedIn Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k}] During evaluation := Solve::nsmet: This system cannot be solved with the methods available to Solve. Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k}] MinValue[{ b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k}] // FullSimplify 1 + Sqrt[2] MaxValue[{ b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k}] // FullSimplify 1 + Sqrt[2]

This is the second step in solving a problem Reygan Dionisio posted on LinkedIn

Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b,
   k}]

During evaluation := Solve::nsmet: This system cannot be solved with the methods available to Solve.

Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b,
   k}]

 MinValue[{ b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, 
   k}] // FullSimplify

1 + Sqrt[2]

MaxValue[{ b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, 
   k}] // FullSimplify

1 + Sqrt[2]

POSTED BY: Frank Kampas

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Neil Singer

Neil Singer, AC Kinetics, Inc.

Posted 2 years ago

Frank, The reason Solve fails is that you have more variables in the equations than you told Solve about. This works (by adding res to the list of variables): Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k, res}] as does this (let Solve figure out the variables): Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}] However, the minimize approach runs faster if you know that the minimum is the solution. Regards, Neil

POSTED BY: Neil Singer

Frank Kampas

Frank Kampas, Physicist at Large Consulting

Posted 2 years ago

MinValue is 100 times faster than Solve In[6]:= AbsoluteTiming[ Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k, res}] // FullSimplify] Out[6]= {84.9759, {{a -> 9^(ArcSinh[1]/Log[5/3]), b -> 15^(ArcSinh[1]/Log[5/3]), k -> ArcSinh[1]/Log[5/3], res -> 1 + Sqrt[2]}}} In[2]:= AbsoluteTiming[ MinValue[{ b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k}] // FullSimplify] Out[2]= {0.399868, 1 + Sqrt[2]}

MinValue is 100 times faster than Solve

In[6]:= AbsoluteTiming[
 Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, 
    b > 0}, {a, b, k, res}] // FullSimplify]

Out[6]= {84.9759, {{a -> 9^(ArcSinh[1]/Log[5/3]), 
   b -> 15^(ArcSinh[1]/Log[5/3]), k -> ArcSinh[1]/Log[5/3], 
   res -> 1 + Sqrt[2]}}}

In[2]:= AbsoluteTiming[
 MinValue[{ b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, 
    b > 0}, {a, b, k}] // FullSimplify]

Out[2]= {0.399868, 1 + Sqrt[2]}

POSTED BY: Frank Kampas