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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 14 hours ago
gagansogaganso
1307
$endgroup$
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 14 hours ago
gagansogaganso
1307
$endgroup$
1
$begingroup$
Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
$endgroup$
– bbgodfrey
14 hours ago
$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
14 hours 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 14 hours ago
gagansogaganso
1307
$endgroup$
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 14 hours ago
gagansogaganso
1307
asked 14 hours ago
gagansogaganso
1307
edited 14 hours ago
gaganso
asked 14 hours ago
gagansogaganso
1307
asked 14 hours ago
gagansogaganso
1307
asked 14 hours ago
gagansogaganso
1307
1307
1
$begingroup$
Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
$endgroup$
– bbgodfrey
14 hours ago
$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
14 hours 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
14 hours ago
$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
14 hours 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
14 hours ago
$begingroup$
Several symbols in your code are undefined. Please provide the definitions to aid the reader in answering your question.
$endgroup$
– bbgodfrey
14 hours ago
$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
14 hours ago
$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
14 hours 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 13 hours ago
bbgodfreybbgodfrey
44.9k958110
$endgroup$
$begingroup$
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
13 hours ago
1
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
13 hours 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 13 hours 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 13 hours ago
bbgodfreybbgodfrey
44.9k958110
$endgroup$
$begingroup$
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
13 hours ago
1
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
13 hours 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 13 hours ago
bbgodfreybbgodfrey
44.9k958110
$endgroup$
$begingroup$
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
13 hours ago
1
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
13 hours 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 13 hours ago
bbgodfreybbgodfrey
44.9k958110
$endgroup$
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 13 hours ago
bbgodfreybbgodfrey
44.9k958110
edited 13 hours ago
answered 13 hours ago
bbgodfreybbgodfrey
44.9k958110
answered 13 hours ago
bbgodfreybbgodfrey
44.9k958110
answered 13 hours ago
bbgodfreybbgodfrey
44.9k958110
44.9k958110
$begingroup$
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
13 hours ago
1
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
13 hours 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
13 hours ago
1
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
13 hours 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
13 hours 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
13 hours ago
1
1
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
13 hours ago
$begingroup$
@gaganso Precisely so.
$endgroup$
– bbgodfrey
13 hours 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 13 hours 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 13 hours 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 13 hours 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 13 hours ago
kglrkglr
187k10203421
edited 13 hours ago
answered 13 hours ago
kglrkglr
187k10203421
answered 13 hours ago
kglrkglr
187k10203421
answered 13 hours 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
14 hours ago
$begingroup$
@bbgodfrey, sorry about that. I have updated the question now.
$endgroup$
– gaganso
14 hours ago