Evaluate Only Part of a Function

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I have a list of functions, each containing none or more of the functions Plus, Times, Subtract and Divide. They could be in any arrangement and with any numbers. This is one such example.

HoldForm[Plus[3+Times[7,Subtract[9,Plus[4,5]],Divide[29,Subtract[4,3]]]]]*

There is an error here, The above should read: Plus[3,Times[7

The numbers can be any positive integer. I need to calculate just the Divide and Subtract functions to find out if they evaluate to 1 or 0 respectively as I consider functions in the list that have this property trivial and I want to filter them out.

I am somewhat a beginner with Wolfram/Mathematica code and I have been attempting to extract the Divide and Subtract parts as a list and then calculating just them parts but so-far my attempts at solving this have been totally unfruitful, partly because I can't know beforehand where the Divide or Subtract functions are in the function or how deep they will be.

Is there a way to accomplish this?

Edit: Just to help clarify what I am trying to achieve. I have a list of functions such as

HoldForm[Plus[3,Times[7,Subtract[9,Plus[4,5]],Divide[29,Subtract[4,3]]]]],
HoldForm[Plus[7,Times[2,Divide[16,Subtract[9,Plus[4,1]]]]]],
HoldForm[Plus[3,Times[7,9],29]]

I need to remove the first element from the list because it is a function that divides by 1 (and subtracts 0), making is only trivially different from the 3rd element of the list. After removing the first function I want to display the output like this

$7+2 frac169-(4+1)$,$3+7times 9+29$

list-manipulation functions replacement symbolic

share|improve this question

edited 2 hours ago

asked 4 hours ago

RedPython

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RedPython is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to Mathematica.SE! Can you please put any code snippets in code blocks to improve the readability of the question?
  – Szabolcs
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  What would be a result of Subtract[9,Plus[4,5]] if Plus is not included in your list?
  – Kuba♦
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In my example, the whole thing should be removed from my list of functions. This is because Subtract[9,Plus[4,5]] will evaluate to 0 and so it means the example is trivial as there will be another function in the list that is the same except it won't Subtract[0]
  – RedPython
  3 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In that case why don't you just evaluate the whole thing and say that the result is 3?
  – Szabolcs
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for the advice Szabolcs. Advice appreciated. I have looked up how to do it and will ensure I follow your advice going forward.
  – RedPython
  3 hours ago
  

  
  
  
  

 | 
show 6 more comments

up vote
5
down vote

favorite

I have a list of functions, each containing none or more of the functions Plus, Times, Subtract and Divide. They could be in any arrangement and with any numbers. This is one such example.

HoldForm[Plus[3+Times[7,Subtract[9,Plus[4,5]],Divide[29,Subtract[4,3]]]]]*

There is an error here, The above should read: Plus[3,Times[7

The numbers can be any positive integer. I need to calculate just the Divide and Subtract functions to find out if they evaluate to 1 or 0 respectively as I consider functions in the list that have this property trivial and I want to filter them out.

I am somewhat a beginner with Wolfram/Mathematica code and I have been attempting to extract the Divide and Subtract parts as a list and then calculating just them parts but so-far my attempts at solving this have been totally unfruitful, partly because I can't know beforehand where the Divide or Subtract functions are in the function or how deep they will be.

Is there a way to accomplish this?

Edit: Just to help clarify what I am trying to achieve. I have a list of functions such as

HoldForm[Plus[3,Times[7,Subtract[9,Plus[4,5]],Divide[29,Subtract[4,3]]]]],
HoldForm[Plus[7,Times[2,Divide[16,Subtract[9,Plus[4,1]]]]]],
HoldForm[Plus[3,Times[7,9],29]]

I need to remove the first element from the list because it is a function that divides by 1 (and subtracts 0), making is only trivially different from the 3rd element of the list. After removing the first function I want to display the output like this

$7+2 frac169-(4+1)$,$3+7times 9+29$

list-manipulation functions replacement symbolic

share|improve this question

edited 2 hours ago

asked 4 hours ago

RedPython

1263

New contributor

RedPython is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to Mathematica.SE! Can you please put any code snippets in code blocks to improve the readability of the question?
  – Szabolcs
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  What would be a result of Subtract[9,Plus[4,5]] if Plus is not included in your list?
  – Kuba♦
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In my example, the whole thing should be removed from my list of functions. This is because Subtract[9,Plus[4,5]] will evaluate to 0 and so it means the example is trivial as there will be another function in the list that is the same except it won't Subtract[0]
  – RedPython
  3 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In that case why don't you just evaluate the whole thing and say that the result is 3?
  – Szabolcs
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for the advice Szabolcs. Advice appreciated. I have looked up how to do it and will ensure I follow your advice going forward.
  – RedPython
  3 hours ago
  

  
  
  
  

 | 
show 6 more comments

up vote
5
down vote

favorite

up vote
5
down vote

favorite

I have a list of functions, each containing none or more of the functions Plus, Times, Subtract and Divide. They could be in any arrangement and with any numbers. This is one such example.

HoldForm[Plus[3+Times[7,Subtract[9,Plus[4,5]],Divide[29,Subtract[4,3]]]]]*

There is an error here, The above should read: Plus[3,Times[7

The numbers can be any positive integer. I need to calculate just the Divide and Subtract functions to find out if they evaluate to 1 or 0 respectively as I consider functions in the list that have this property trivial and I want to filter them out.

I am somewhat a beginner with Wolfram/Mathematica code and I have been attempting to extract the Divide and Subtract parts as a list and then calculating just them parts but so-far my attempts at solving this have been totally unfruitful, partly because I can't know beforehand where the Divide or Subtract functions are in the function or how deep they will be.

Is there a way to accomplish this?

Edit: Just to help clarify what I am trying to achieve. I have a list of functions such as

HoldForm[Plus[3,Times[7,Subtract[9,Plus[4,5]],Divide[29,Subtract[4,3]]]]],
HoldForm[Plus[7,Times[2,Divide[16,Subtract[9,Plus[4,1]]]]]],
HoldForm[Plus[3,Times[7,9],29]]

I need to remove the first element from the list because it is a function that divides by 1 (and subtracts 0), making is only trivially different from the 3rd element of the list. After removing the first function I want to display the output like this

$7+2 frac169-(4+1)$,$3+7times 9+29$

list-manipulation functions replacement symbolic

share|improve this question

edited 2 hours ago

asked 4 hours ago

RedPython

1263

New contributor

RedPython is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

I have a list of functions, each containing none or more of the functions Plus, Times, Subtract and Divide. They could be in any arrangement and with any numbers. This is one such example.

HoldForm[Plus[3+Times[7,Subtract[9,Plus[4,5]],Divide[29,Subtract[4,3]]]]]*

There is an error here, The above should read: Plus[3,Times[7

The numbers can be any positive integer. I need to calculate just the Divide and Subtract functions to find out if they evaluate to 1 or 0 respectively as I consider functions in the list that have this property trivial and I want to filter them out.

I am somewhat a beginner with Wolfram/Mathematica code and I have been attempting to extract the Divide and Subtract parts as a list and then calculating just them parts but so-far my attempts at solving this have been totally unfruitful, partly because I can't know beforehand where the Divide or Subtract functions are in the function or how deep they will be.

Is there a way to accomplish this?

Edit: Just to help clarify what I am trying to achieve. I have a list of functions such as

HoldForm[Plus[3,Times[7,Subtract[9,Plus[4,5]],Divide[29,Subtract[4,3]]]]],
HoldForm[Plus[7,Times[2,Divide[16,Subtract[9,Plus[4,1]]]]]],
HoldForm[Plus[3,Times[7,9],29]]

I need to remove the first element from the list because it is a function that divides by 1 (and subtracts 0), making is only trivially different from the 3rd element of the list. After removing the first function I want to display the output like this

$7+2 frac169-(4+1)$,$3+7times 9+29$

list-manipulation functions replacement symbolic

list-manipulation functions replacement symbolic

share|improve this question

edited 2 hours ago

asked 4 hours ago

RedPython

1263

New contributor

RedPython is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

edited 2 hours ago

asked 4 hours ago

RedPython

1263

New contributor

RedPython is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

share|improve this question

edited 2 hours ago

edited 2 hours ago

edited 2 hours ago

asked 4 hours ago

RedPython

1263

New contributor

RedPython is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 4 hours ago

RedPython

1263

asked 4 hours ago

RedPython

1263

1263

New contributor

RedPython is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

New contributor

RedPython is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

RedPython is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to Mathematica.SE! Can you please put any code snippets in code blocks to improve the readability of the question?
  – Szabolcs
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  What would be a result of Subtract[9,Plus[4,5]] if Plus is not included in your list?
  – Kuba♦
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In my example, the whole thing should be removed from my list of functions. This is because Subtract[9,Plus[4,5]] will evaluate to 0 and so it means the example is trivial as there will be another function in the list that is the same except it won't Subtract[0]
  – RedPython
  3 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In that case why don't you just evaluate the whole thing and say that the result is 3?
  – Szabolcs
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for the advice Szabolcs. Advice appreciated. I have looked up how to do it and will ensure I follow your advice going forward.
  – RedPython
  3 hours ago
  

  
  
  
  

 | 
show 6 more comments

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to Mathematica.SE! Can you please put any code snippets in code blocks to improve the readability of the question?
  – Szabolcs
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  What would be a result of Subtract[9,Plus[4,5]] if Plus is not included in your list?
  – Kuba♦
  4 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In my example, the whole thing should be removed from my list of functions. This is because Subtract[9,Plus[4,5]] will evaluate to 0 and so it means the example is trivial as there will be another function in the list that is the same except it won't Subtract[0]
  – RedPython
  3 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  In that case why don't you just evaluate the whole thing and say that the result is 3?
  – Szabolcs
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for the advice Szabolcs. Advice appreciated. I have looked up how to do it and will ensure I follow your advice going forward.
  – RedPython
  3 hours ago
  

  
  
  
  

Welcome to Mathematica.SE! Can you please put any code snippets in code blocks to improve the readability of the question?
– Szabolcs
4 hours ago

Welcome to Mathematica.SE! Can you please put any code snippets in code blocks to improve the readability of the question?
– Szabolcs
4 hours ago

1

1

What would be a result of Subtract[9,Plus[4,5]] if Plus is not included in your list?
– Kuba♦
4 hours ago

What would be a result of Subtract[9,Plus[4,5]] if Plus is not included in your list?
– Kuba♦
4 hours ago

In my example, the whole thing should be removed from my list of functions. This is because Subtract[9,Plus[4,5]] will evaluate to 0 and so it means the example is trivial as there will be another function in the list that is the same except it won't Subtract[0]
– RedPython
3 hours ago

In my example, the whole thing should be removed from my list of functions. This is because Subtract[9,Plus[4,5]] will evaluate to 0 and so it means the example is trivial as there will be another function in the list that is the same except it won't Subtract[0]
– RedPython
3 hours ago

In that case why don't you just evaluate the whole thing and say that the result is 3?
– Szabolcs
3 hours ago

In that case why don't you just evaluate the whole thing and say that the result is 3?
– Szabolcs
3 hours ago

Thanks for the advice Szabolcs. Advice appreciated. I have looked up how to do it and will ensure I follow your advice going forward.
– RedPython
3 hours ago

Thanks for the advice Szabolcs. Advice appreciated. I have looked up how to do it and will ensure I follow your advice going forward.
– RedPython
3 hours ago

 | 
show 6 more comments

2 Answers
2

active

oldest

votes

up vote
5
down vote

exp = Inactivate[Plus[3 + Times[7, Subtract[9, Plus[4, 5]], Divide[29, Subtract[4, 3]]]]];
Activate[exp, Divide | Subtract]

Inactive[Plus][3 + 7*(9 - (4 + 5))*29]

An alternative way to evaluate completely subexpressions with head Divide or Subtract
using RuleCondition (from WReach's answer in the q/a linked in Sjoerd's answer):

HoldForm[Plus[3 + Times[7, Subtract[9, Plus[4, 5]], Divide[29, Subtract[4, 3]]]]] /. 
 e : _Subtract | _Divide :> RuleCondition[e]

+(3 + 7 0 29)

share|improve this answer

edited 3 hours ago

answered 4 hours ago

kglr

160k8184384

add a comment | 

up vote
4
down vote

The answer of kglr works if you only want to do the evaluations associated with Divide and Subtract. If instead you want every subexpression with these head to evaluate completely, use the following trick:

Hold[
 Plus[
 3 + Times[7, Subtract[9, Plus[4, 5]], 
 Divide[29, Subtract[4, 3]]]]
] /. 
 expr : (_Divide 

See also the following answer:

Replacement inside held expression

share|improve this answer

edited 2 hours ago

answered 3 hours ago

Sjoerd Smit

2,670414

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

up vote
5
down vote

exp = Inactivate[Plus[3 + Times[7, Subtract[9, Plus[4, 5]], Divide[29, Subtract[4, 3]]]]];
Activate[exp, Divide | Subtract]

Inactive[Plus][3 + 7*(9 - (4 + 5))*29]

An alternative way to evaluate completely subexpressions with head Divide or Subtract
using RuleCondition (from WReach's answer in the q/a linked in Sjoerd's answer):

HoldForm[Plus[3 + Times[7, Subtract[9, Plus[4, 5]], Divide[29, Subtract[4, 3]]]]] /. 
 e : _Subtract | _Divide :> RuleCondition[e]

+(3 + 7 0 29)

share|improve this answer

edited 3 hours ago

answered 4 hours ago

kglr

160k8184384

add a comment | 

up vote
5
down vote

exp = Inactivate[Plus[3 + Times[7, Subtract[9, Plus[4, 5]], Divide[29, Subtract[4, 3]]]]];
Activate[exp, Divide | Subtract]

Inactive[Plus][3 + 7*(9 - (4 + 5))*29]

An alternative way to evaluate completely subexpressions with head Divide or Subtract
using RuleCondition (from WReach's answer in the q/a linked in Sjoerd's answer):

HoldForm[Plus[3 + Times[7, Subtract[9, Plus[4, 5]], Divide[29, Subtract[4, 3]]]]] /. 
 e : _Subtract | _Divide :> RuleCondition[e]

+(3 + 7 0 29)

share|improve this answer

edited 3 hours ago

answered 4 hours ago

kglr

160k8184384

add a comment | 

up vote
5
down vote

up vote
5
down vote

exp = Inactivate[Plus[3 + Times[7, Subtract[9, Plus[4, 5]], Divide[29, Subtract[4, 3]]]]];
Activate[exp, Divide | Subtract]

Inactive[Plus][3 + 7*(9 - (4 + 5))*29]

An alternative way to evaluate completely subexpressions with head Divide or Subtract
using RuleCondition (from WReach's answer in the q/a linked in Sjoerd's answer):

HoldForm[Plus[3 + Times[7, Subtract[9, Plus[4, 5]], Divide[29, Subtract[4, 3]]]]] /. 
 e : _Subtract | _Divide :> RuleCondition[e]

+(3 + 7 0 29)

share|improve this answer

edited 3 hours ago

answered 4 hours ago

kglr

160k8184384

exp = Inactivate[Plus[3 + Times[7, Subtract[9, Plus[4, 5]], Divide[29, Subtract[4, 3]]]]];
Activate[exp, Divide | Subtract]

Inactive[Plus][3 + 7*(9 - (4 + 5))*29]

An alternative way to evaluate completely subexpressions with head Divide or Subtract
using RuleCondition (from WReach's answer in the q/a linked in Sjoerd's answer):

HoldForm[Plus[3 + Times[7, Subtract[9, Plus[4, 5]], Divide[29, Subtract[4, 3]]]]] /. 
 e : _Subtract | _Divide :> RuleCondition[e]

+(3 + 7 0 29)

share|improve this answer

edited 3 hours ago

answered 4 hours ago

kglr

160k8184384

share|improve this answer

share|improve this answer

edited 3 hours ago

edited 3 hours ago

edited 3 hours ago

answered 4 hours ago

kglr

160k8184384

answered 4 hours ago

kglr

160k8184384

answered 4 hours ago

kglr

160k8184384

160k8184384

add a comment | 

add a comment | 

up vote
4
down vote

The answer of kglr works if you only want to do the evaluations associated with Divide and Subtract. If instead you want every subexpression with these head to evaluate completely, use the following trick:

Hold[
 Plus[
 3 + Times[7, Subtract[9, Plus[4, 5]], 
 Divide[29, Subtract[4, 3]]]]
] /. 
 expr : (_Divide 

See also the following answer:

Replacement inside held expression

share|improve this answer

edited 2 hours ago

answered 3 hours ago

Sjoerd Smit

2,670414

add a comment | 

up vote
4
down vote

The answer of kglr works if you only want to do the evaluations associated with Divide and Subtract. If instead you want every subexpression with these head to evaluate completely, use the following trick:

Hold[
 Plus[
 3 + Times[7, Subtract[9, Plus[4, 5]], 
 Divide[29, Subtract[4, 3]]]]
] /. 
 expr : (_Divide 

See also the following answer:

Replacement inside held expression

share|improve this answer

edited 2 hours ago

answered 3 hours ago

Sjoerd Smit

2,670414

add a comment | 

up vote
4
down vote

up vote
4
down vote

The answer of kglr works if you only want to do the evaluations associated with Divide and Subtract. If instead you want every subexpression with these head to evaluate completely, use the following trick:

Hold[
 Plus[
 3 + Times[7, Subtract[9, Plus[4, 5]], 
 Divide[29, Subtract[4, 3]]]]
] /. 
 expr : (_Divide 

See also the following answer:

Replacement inside held expression

share|improve this answer

edited 2 hours ago

answered 3 hours ago

Sjoerd Smit

2,670414

The answer of kglr works if you only want to do the evaluations associated with Divide and Subtract. If instead you want every subexpression with these head to evaluate completely, use the following trick:

Hold[
 Plus[
 3 + Times[7, Subtract[9, Plus[4, 5]], 
 Divide[29, Subtract[4, 3]]]]
] /. 
 expr : (_Divide 

See also the following answer:

Replacement inside held expression

share|improve this answer

edited 2 hours ago

answered 3 hours ago

Sjoerd Smit

2,670414

share|improve this answer

share|improve this answer

edited 2 hours ago

edited 2 hours ago

edited 2 hours ago

answered 3 hours ago

Sjoerd Smit

2,670414

answered 3 hours ago

Sjoerd Smit

2,670414

answered 3 hours ago

Sjoerd Smit

2,670414

2,670414

add a comment | 

add a comment | 

RedPython is a new contributor. Be nice, and check out our Code of Conduct.

 

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