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Find maximum of the output from reduce
How Can I use Solve/Reduce OutputFailure message from ReduceExtract desired solutions from ReduceFinding the least positive integer satisfying a quantified statementhow do I control the output of Reduce function?Using the output of ReduceIncomplete and weird output from ReduceUsing Solve returns unnecessary Root, overcomplicated formula, and erroneous negative valueHow to analyse huge output from Reduce systematically?Make Reduce produce nicer output
$begingroup$
I am trying to reduce a function in two variables($n_1$ and $n_2$) whose domain is the set of Integers. I get a long list of pairs of values for these two variables(instead of a range). This could be because the range of $n_2$ changes for each $n_1$. I just want the maximum value of $n_1$ and $n_2$. Can you please guide me?
driftParamSet = 1.9 - 0.2 Subscript[n, 2] + Subscript[n, 1] (-0.2 + (2.91434*10^-16 Subscript[n, 1])/(1. Subscript[n, 1] + 1.5 Subscript[n, 2]));
drift[Gamma] = 17;
Reduce[driftParamSet> -drift[Gamma] && Subscript[n, 1]>= 0 && Subscript[n, 2]>= 0,{Subscript[n, 1],Subscript[n, 2]}, Integers];
Current output:
$n_1=0land n_2=1left|n_1=0land n_2=2right|n_1=0land n_2=3|n_1=0land n_2=4
\......\left|n_1=0land n_2=90right|n_1=0land n_2=91|\.....\
left(n_1=92land n_2=2right)lor left(n_1=93land n_2=0right)lor left(n_1=93land n_2=1right)lor left(n_1=94land n_2=0right)$
Expected output:
$n_1$=94 and $n_2=$91
equation-solving functions
asked 2 hours ago
gagansogaganso
1207
$endgroup$
add a comment |
$begingroup$
I am trying to reduce a function in two variables($n_1$ and $n_2$) whose domain is the set of Integers. I get a long list of pairs of values for these two variables(instead of a range). This could be because the range of $n_2$ changes for each $n_1$. I just want the maximum value of $n_1$ and $n_2$. Can you please guide me?
driftParamSet = 1.9 - 0.2 Subscript[n, 2] + Subscript[n, 1] (-0.2 + (2.91434*10^-16 Subscript[n, 1])/(1. Subscript[n, 1] + 1.5 Subscript[n, 2]));
drift[Gamma] = 17;
Reduce[driftParamSet> -drift[Gamma] && Subscript[n, 1]>= 0 && Subscript[n, 2]>= 0,{Subscript[n, 1],Subscript[n, 2]}, Integers];
Current output:
$n_1=0land n_2=1left|n_1=0land n_2=2right|n_1=0land n_2=3|n_1=0land n_2=4
\......\left|n_1=0land n_2=90right|n_1=0land n_2=91|\.....\
left(n_1=92land n_2=2right)lor left(n_1=93land n_2=0right)lor left(n_1=93land n_2=1right)lor left(n_1=94land n_2=0right)$
Expected output:
$n_1$=94 and $n_2=$91
equation-solving functions
asked 2 hours ago
gagansogaganso
1207
$endgroup$
1
$begingroup$
Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
$endgroup$
– bbgodfrey
1 hour ago
$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
1 hour ago
add a comment |
$begingroup$
I am trying to reduce a function in two variables($n_1$ and $n_2$) whose domain is the set of Integers. I get a long list of pairs of values for these two variables(instead of a range). This could be because the range of $n_2$ changes for each $n_1$. I just want the maximum value of $n_1$ and $n_2$. Can you please guide me?
driftParamSet = 1.9 - 0.2 Subscript[n, 2] + Subscript[n, 1] (-0.2 + (2.91434*10^-16 Subscript[n, 1])/(1. Subscript[n, 1] + 1.5 Subscript[n, 2]));
drift[Gamma] = 17;
Reduce[driftParamSet> -drift[Gamma] && Subscript[n, 1]>= 0 && Subscript[n, 2]>= 0,{Subscript[n, 1],Subscript[n, 2]}, Integers];
Current output:
$n_1=0land n_2=1left|n_1=0land n_2=2right|n_1=0land n_2=3|n_1=0land n_2=4
\......\left|n_1=0land n_2=90right|n_1=0land n_2=91|\.....\
left(n_1=92land n_2=2right)lor left(n_1=93land n_2=0right)lor left(n_1=93land n_2=1right)lor left(n_1=94land n_2=0right)$
Expected output:
$n_1$=94 and $n_2=$91
equation-solving functions
asked 2 hours ago
gagansogaganso
1207
$endgroup$
I am trying to reduce a function in two variables($n_1$ and $n_2$) whose domain is the set of Integers. I get a long list of pairs of values for these two variables(instead of a range). This could be because the range of $n_2$ changes for each $n_1$. I just want the maximum value of $n_1$ and $n_2$. Can you please guide me?
driftParamSet = 1.9 - 0.2 Subscript[n, 2] + Subscript[n, 1] (-0.2 + (2.91434*10^-16 Subscript[n, 1])/(1. Subscript[n, 1] + 1.5 Subscript[n, 2]));
drift[Gamma] = 17;
Reduce[driftParamSet> -drift[Gamma] && Subscript[n, 1]>= 0 && Subscript[n, 2]>= 0,{Subscript[n, 1],Subscript[n, 2]}, Integers];
Current output:
$n_1=0land n_2=1left|n_1=0land n_2=2right|n_1=0land n_2=3|n_1=0land n_2=4
\......\left|n_1=0land n_2=90right|n_1=0land n_2=91|\.....\
left(n_1=92land n_2=2right)lor left(n_1=93land n_2=0right)lor left(n_1=93land n_2=1right)lor left(n_1=94land n_2=0right)$
Expected output:
$n_1$=94 and $n_2=$91
equation-solving functions
equation-solving functions
asked 2 hours ago
gagansogaganso
1207
asked 2 hours ago
gagansogaganso
1207
edited 1 hour ago
gaganso
asked 2 hours ago
gagansogaganso
1207
asked 2 hours ago
gagansogaganso
1207
asked 2 hours ago
gagansogaganso
1207
1207
1
$begingroup$
Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
$endgroup$
– bbgodfrey
1 hour ago
$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
1 hour ago
add a comment |
1
$begingroup$
Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
$endgroup$
– bbgodfrey
1 hour ago
$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
1 hour ago
1
1
$begingroup$
Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
$endgroup$
– bbgodfrey
1 hour ago
$begingroup$
Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
$endgroup$
– bbgodfrey
1 hour ago
$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
1 hour ago
$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
1 hour ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Let the large result of Reduce be rs. Then the maximum of each quantity is determined by
Max@Cases[rs, Equal[Subscript[n, 1], z_] -> z, Infinity]
(* 94 *)
Max@Cases[rs, Equal[Subscript[n, 2], z_] -> z, Infinity]
(* 94 *)
not 91 as speculated in the question. The corresponding terms in rs can be obtained by
Position[rs, 94, Infinity]
(* {{94, 2, 2}, {4559, 1, 2}} *)
rs[[94]]
(* Subscript[n, 1] == 0 && Subscript[n, 2] == 94 *)
rs[[4559]]
(* Subscript[n, 1] == 94 && Subscript[n, 2] == 0 *)
answered 1 hour ago
bbgodfreybbgodfrey
44.8k958110
$endgroup$
$begingroup$
thank you! To understand this better, the Cases[] function with the specified parameter creates a list of values of n1/n2 and the Max[] function operates on this list to give the maximum?
$endgroup$
– gaganso
1 hour ago
1
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
1 hour ago
add a comment |
$begingroup$
An alternative is to use Solve after Rationalizeing input expressions:
driftParamSet = Rationalize[1.9 - 0.2 n2 +
n1 (-0.2 + (2.91434*10^-16 n1)/(1. n1 + 1.5 n2)), 10^-16]
driftγ = 17;
solutions = Solve[driftParamSet > -driftγ && n1 >= 0 && n2 >= 0, {n1, n2}, Integers];
Max /@ Transpose[{n1, n2} /. solutions]
{94, 94}
Yet another approach is using ArgMax:
Extract[ArgMax[{#, driftParamSet > -driftγ && n1 >= 0 && n2 >= 0}, {n1, n2}, Integers]& /@
{n1, n2}, {{1, 1}, {-1, -1}}]
{94, 94}
answered 1 hour ago
kglrkglr
187k10203421
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Let the large result of Reduce be rs. Then the maximum of each quantity is determined by
Max@Cases[rs, Equal[Subscript[n, 1], z_] -> z, Infinity]
(* 94 *)
Max@Cases[rs, Equal[Subscript[n, 2], z_] -> z, Infinity]
(* 94 *)
not 91 as speculated in the question. The corresponding terms in rs can be obtained by
Position[rs, 94, Infinity]
(* {{94, 2, 2}, {4559, 1, 2}} *)
rs[[94]]
(* Subscript[n, 1] == 0 && Subscript[n, 2] == 94 *)
rs[[4559]]
(* Subscript[n, 1] == 94 && Subscript[n, 2] == 0 *)
answered 1 hour ago
bbgodfreybbgodfrey
44.8k958110
$endgroup$
$begingroup$
thank you! To understand this better, the Cases[] function with the specified parameter creates a list of values of n1/n2 and the Max[] function operates on this list to give the maximum?
$endgroup$
– gaganso
1 hour ago
1
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
1 hour ago
add a comment |
$begingroup$
Let the large result of Reduce be rs. Then the maximum of each quantity is determined by
Max@Cases[rs, Equal[Subscript[n, 1], z_] -> z, Infinity]
(* 94 *)
Max@Cases[rs, Equal[Subscript[n, 2], z_] -> z, Infinity]
(* 94 *)
not 91 as speculated in the question. The corresponding terms in rs can be obtained by
Position[rs, 94, Infinity]
(* {{94, 2, 2}, {4559, 1, 2}} *)
rs[[94]]
(* Subscript[n, 1] == 0 && Subscript[n, 2] == 94 *)
rs[[4559]]
(* Subscript[n, 1] == 94 && Subscript[n, 2] == 0 *)
answered 1 hour ago
bbgodfreybbgodfrey
44.8k958110
$endgroup$
$begingroup$
thank you! To understand this better, the Cases[] function with the specified parameter creates a list of values of n1/n2 and the Max[] function operates on this list to give the maximum?
$endgroup$
– gaganso
1 hour ago
1
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
1 hour ago
add a comment |
$begingroup$
Let the large result of Reduce be rs. Then the maximum of each quantity is determined by
Max@Cases[rs, Equal[Subscript[n, 1], z_] -> z, Infinity]
(* 94 *)
Max@Cases[rs, Equal[Subscript[n, 2], z_] -> z, Infinity]
(* 94 *)
not 91 as speculated in the question. The corresponding terms in rs can be obtained by
Position[rs, 94, Infinity]
(* {{94, 2, 2}, {4559, 1, 2}} *)
rs[[94]]
(* Subscript[n, 1] == 0 && Subscript[n, 2] == 94 *)
rs[[4559]]
(* Subscript[n, 1] == 94 && Subscript[n, 2] == 0 *)
answered 1 hour ago
bbgodfreybbgodfrey
44.8k958110
$endgroup$
Let the large result of Reduce be rs. Then the maximum of each quantity is determined by
Max@Cases[rs, Equal[Subscript[n, 1], z_] -> z, Infinity]
(* 94 *)
Max@Cases[rs, Equal[Subscript[n, 2], z_] -> z, Infinity]
(* 94 *)
not 91 as speculated in the question. The corresponding terms in rs can be obtained by
Position[rs, 94, Infinity]
(* {{94, 2, 2}, {4559, 1, 2}} *)
rs[[94]]
(* Subscript[n, 1] == 0 && Subscript[n, 2] == 94 *)
rs[[4559]]
(* Subscript[n, 1] == 94 && Subscript[n, 2] == 0 *)
answered 1 hour ago
bbgodfreybbgodfrey
44.8k958110
edited 1 hour ago
answered 1 hour ago
bbgodfreybbgodfrey
44.8k958110
answered 1 hour ago
bbgodfreybbgodfrey
44.8k958110
answered 1 hour ago
bbgodfreybbgodfrey
44.8k958110
44.8k958110
$begingroup$
thank you! To understand this better, the Cases[] function with the specified parameter creates a list of values of n1/n2 and the Max[] function operates on this list to give the maximum?
$endgroup$
– gaganso
1 hour ago
1
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
1 hour ago
add a comment |
$begingroup$
thank you! To understand this better, the Cases[] function with the specified parameter creates a list of values of n1/n2 and the Max[] function operates on this list to give the maximum?
$endgroup$
– gaganso
1 hour ago
1
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
1 hour ago
$begingroup$
thank you! To understand this better, the Cases[] function with the specified parameter creates a list of values of n1/n2 and the Max[] function operates on this list to give the maximum?
$endgroup$
– gaganso
1 hour ago
$begingroup$
thank you! To understand this better, the Cases[] function with the specified parameter creates a list of values of n1/n2 and the Max[] function operates on this list to give the maximum?
$endgroup$
– gaganso
1 hour ago
1
1
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
1 hour ago
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
1 hour ago
add a comment |
$begingroup$
An alternative is to use Solve after Rationalizeing input expressions:
driftParamSet = Rationalize[1.9 - 0.2 n2 +
n1 (-0.2 + (2.91434*10^-16 n1)/(1. n1 + 1.5 n2)), 10^-16]
driftγ = 17;
solutions = Solve[driftParamSet > -driftγ && n1 >= 0 && n2 >= 0, {n1, n2}, Integers];
Max /@ Transpose[{n1, n2} /. solutions]
{94, 94}
Yet another approach is using ArgMax:
Extract[ArgMax[{#, driftParamSet > -driftγ && n1 >= 0 && n2 >= 0}, {n1, n2}, Integers]& /@
{n1, n2}, {{1, 1}, {-1, -1}}]
{94, 94}
answered 1 hour ago
kglrkglr
187k10203421
$endgroup$
add a comment |
$begingroup$
An alternative is to use Solve after Rationalizeing input expressions:
driftParamSet = Rationalize[1.9 - 0.2 n2 +
n1 (-0.2 + (2.91434*10^-16 n1)/(1. n1 + 1.5 n2)), 10^-16]
driftγ = 17;
solutions = Solve[driftParamSet > -driftγ && n1 >= 0 && n2 >= 0, {n1, n2}, Integers];
Max /@ Transpose[{n1, n2} /. solutions]
{94, 94}
Yet another approach is using ArgMax:
Extract[ArgMax[{#, driftParamSet > -driftγ && n1 >= 0 && n2 >= 0}, {n1, n2}, Integers]& /@
{n1, n2}, {{1, 1}, {-1, -1}}]
{94, 94}
answered 1 hour ago
kglrkglr
187k10203421
$endgroup$
add a comment |
$begingroup$
An alternative is to use Solve after Rationalizeing input expressions:
driftParamSet = Rationalize[1.9 - 0.2 n2 +
n1 (-0.2 + (2.91434*10^-16 n1)/(1. n1 + 1.5 n2)), 10^-16]
driftγ = 17;
solutions = Solve[driftParamSet > -driftγ && n1 >= 0 && n2 >= 0, {n1, n2}, Integers];
Max /@ Transpose[{n1, n2} /. solutions]
{94, 94}
Yet another approach is using ArgMax:
Extract[ArgMax[{#, driftParamSet > -driftγ && n1 >= 0 && n2 >= 0}, {n1, n2}, Integers]& /@
{n1, n2}, {{1, 1}, {-1, -1}}]
{94, 94}
answered 1 hour ago
kglrkglr
187k10203421
$endgroup$
An alternative is to use Solve after Rationalizeing input expressions:
driftParamSet = Rationalize[1.9 - 0.2 n2 +
n1 (-0.2 + (2.91434*10^-16 n1)/(1. n1 + 1.5 n2)), 10^-16]
driftγ = 17;
solutions = Solve[driftParamSet > -driftγ && n1 >= 0 && n2 >= 0, {n1, n2}, Integers];
Max /@ Transpose[{n1, n2} /. solutions]
{94, 94}
Yet another approach is using ArgMax:
Extract[ArgMax[{#, driftParamSet > -driftγ && n1 >= 0 && n2 >= 0}, {n1, n2}, Integers]& /@
{n1, n2}, {{1, 1}, {-1, -1}}]
{94, 94}
answered 1 hour ago
kglrkglr
187k10203421
edited 49 mins ago
answered 1 hour ago
kglrkglr
187k10203421
answered 1 hour ago
kglrkglr
187k10203421
answered 1 hour ago
kglrkglr
187k10203421
187k10203421
add a comment |
add a comment |
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1
$begingroup$
Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
$endgroup$
– bbgodfrey
1 hour ago
$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
1 hour ago