Revisions to Quick way to use conditioned patterns when defining multi-argument function?

In order to make the Clear[f4] useful, I append 4 to f.

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edit approved Jun 11, 2020 at 10:16

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I have a simple function that is supposed to only accept numeric values (i.e. complex/real numbers and constant symbols e.g. Pi, E).

$$f(a,b,c)=a+b+c$$

Edit: I should have chosen a less simple function for this question as there might be approaches that will work for this simple function but not for functions in general (1-see end of question). Please think of a more complicated function, such as $$f(a,b,c)=a^2 \sin(b) \log(c)$$ when you're thinking of an answer.

I know that one can use _?NumericQ for each parameter such that only numeric values of that parameters are entered into the function (click here for more information on putting constrains on patterns).

Clear[f1]
f1[a_?NumericQ, b_?NumericQ, c_?NumericQ] := a + b + c

f1 @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}
(* {6, f[x, y, z], f[1, y, z], f[x, 2, z], f[x, y, 3]} *)

However, for functions with more than 1 variables, I'm way too lazy to add NumericQ after each parameter. Using /; at the end of the function definition works, but I feel it's still too long and I have to retype the name of the parameters (a,b,c) at the end.

Clear[f2, f3]
f2[a_, b_, c_] := a + b + c /; And @@ (NumericQ[#] & /@ {a, b, c})
f3[a_, b_, c_] := a + b + c /; VectorQ[{a, b, c}, NumericQ]

Is there any way to express the condition only once, and without having to type the list of parameters one more time? I know that this is a frivolous question borne out of sheer laziness but I'd love to hear your ideas.

(1) such as using the double underscore (BlankSequence) to apply NumericQ to any number of arguments passed to Plus (per Kuba's helpful suggestion). This is because these arguments have identical hierarchy in the function--thus having no need for parameters with different names to represent them--and because Plus can take any number of arguments.

Clear[f4]
f[a__f4[a__?NumericQ] := Plus[a]
 
ff4 @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}    
(* {6,f[xf4[x,y,z],f[1f4[1,y,z],f[xf4[x,2,z],f[xf4[x,y,3]} *)

I have a simple function that is supposed to only accept numeric values (i.e. complex/real numbers and constant symbols e.g. Pi, E).

$$f(a,b,c)=a+b+c$$

Edit: I should have chosen a less simple function for this question as there might be approaches that will work for this simple function but not for functions in general (1-see end of question). Please think of a more complicated function, such as $$f(a,b,c)=a^2 \sin(b) \log(c)$$ when you're thinking of an answer.

I know that one can use _?NumericQ for each parameter such that only numeric values of that parameters are entered into the function (click here for more information on putting constrains on patterns).

Clear[f1]
f1[a_?NumericQ, b_?NumericQ, c_?NumericQ] := a + b + c

f1 @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}
(* {6, f[x, y, z], f[1, y, z], f[x, 2, z], f[x, y, 3]} *)

However, for functions with more than 1 variables, I'm way too lazy to add NumericQ after each parameter. Using /; at the end of the function definition works, but I feel it's still too long and I have to retype the name of the parameters (a,b,c) at the end.

Clear[f2, f3]
f2[a_, b_, c_] := a + b + c /; And @@ (NumericQ[#] & /@ {a, b, c})
f3[a_, b_, c_] := a + b + c /; VectorQ[{a, b, c}, NumericQ]

Is there any way to express the condition only once, and without having to type the list of parameters one more time? I know that this is a frivolous question borne out of sheer laziness but I'd love to hear your ideas.

(1) such as using the double underscore (BlankSequence) to apply NumericQ to any number of arguments passed to Plus (per Kuba's helpful suggestion). This is because these arguments have identical hierarchy in the function--thus having no need for parameters with different names to represent them--and because Plus can take any number of arguments.

Clear[f4]
f[a__?NumericQ] := Plus[a]
 
f @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}    
(* {6,f[x,y,z],f[1,y,z],f[x,2,z],f[x,y,3]} *)

I have a simple function that is supposed to only accept numeric values (i.e. complex/real numbers and constant symbols e.g. Pi, E).

$$f(a,b,c)=a+b+c$$

Edit: I should have chosen a less simple function for this question as there might be approaches that will work for this simple function but not for functions in general (1-see end of question). Please think of a more complicated function, such as $$f(a,b,c)=a^2 \sin(b) \log(c)$$ when you're thinking of an answer.

I know that one can use _?NumericQ for each parameter such that only numeric values of that parameters are entered into the function (click here for more information on putting constrains on patterns).

Clear[f1]
f1[a_?NumericQ, b_?NumericQ, c_?NumericQ] := a + b + c

f1 @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}
(* {6, f[x, y, z], f[1, y, z], f[x, 2, z], f[x, y, 3]} *)

However, for functions with more than 1 variables, I'm way too lazy to add NumericQ after each parameter. Using /; at the end of the function definition works, but I feel it's still too long and I have to retype the name of the parameters (a,b,c) at the end.

Clear[f2, f3]
f2[a_, b_, c_] := a + b + c /; And @@ (NumericQ[#] & /@ {a, b, c})
f3[a_, b_, c_] := a + b + c /; VectorQ[{a, b, c}, NumericQ]

Is there any way to express the condition only once, and without having to type the list of parameters one more time? I know that this is a frivolous question borne out of sheer laziness but I'd love to hear your ideas.

(1) such as using the double underscore (BlankSequence) to apply NumericQ to any number of arguments passed to Plus (per Kuba's helpful suggestion). This is because these arguments have identical hierarchy in the function--thus having no need for parameters with different names to represent them--and because Plus can take any number of arguments.

Clear[f4]
f4[a__?NumericQ] := Plus[a]
 
f4 @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}    
(* {6,f4[x,y,z],f4[1,y,z],f4[x,2,z],f4[x,y,3]} *)

added 2 characters in body

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edited Jun 24, 2015 at 1:18

J. M.'s missing motivation ♦

125.5k
11
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581

I have a simple function that is supposed to only accept numeric values (i.e. complex/real numbers and constant symbols e.g. Pi, E).

$$f(a,b,c)=a+b+c$$

Edit: I should have chosen a less simple function for this question as there might be approaches that will work for this simple function but not for functions in general (1-see end of question). Please think of a more complicated function, such as $$f(a,b,c)=a^2 sin(b) log(c)$$$$f(a,b,c)=a^2 \sin(b) \log(c)$$ when you're thinking of an answer.

I know that one can use _?NumericQ for each parameter such that only numeric values of that parameters are entered into the function (click here for more information on putting constrains on patterns).

Clear[f1]
f1[a_?NumericQ, b_?NumericQ, c_?NumericQ] := a + b + c

f1 @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}
(* {6, f[x, y, z], f[1, y, z], f[x, 2, z], f[x, y, 3]} *)

However, for functions with more than 1 variables, I'm way too lazy to add NumericQ after each parameter. Using /; at the end of the function definition works, but I feel it's still too long and I have to retype the name of the parameters (a,b,c) at the end.

Clear[f2, f3]
f2[a_, b_, c_] := a + b + c /; And @@ (NumericQ[#] & /@ {a, b, c})
f3[a_, b_, c_] := a + b + c /; VectorQ[{a, b, c}, NumericQ]

Is there any way to express the condition only once, and without having to type the list of parameters one more time? I know that this is a frivolous question borne out of sheer laziness but I'd love to hear your ideas.

(1) such as using the double underscore (BlankSequence) to apply NumericQ to any number of arguments passed to Plus (per Kuba's helpful suggestion). This is because these arguments have identical hierarchy in the function--thus having no need for parameters with different names to represent them--and because Plus can take any number of arguments.

Clear[f4]
f[a__?NumericQ] := Plus[a]
 
f @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}    
(* {6,f[x,y,z],f[1,y,z],f[x,2,z],f[x,y,3]} *)

I have a simple function that is supposed to only accept numeric values (i.e. complex/real numbers and constant symbols e.g. Pi, E).

$$f(a,b,c)=a+b+c$$

Edit: I should have chosen a less simple function for this question as there might be approaches that will work for this simple function but not for functions in general (1-see end of question). Please think of a more complicated function, such as $$f(a,b,c)=a^2 sin(b) log(c)$$ when you're thinking of an answer.

I know that one can use _?NumericQ for each parameter such that only numeric values of that parameters are entered into the function (click here for more information on putting constrains on patterns).

Clear[f1]
f1[a_?NumericQ, b_?NumericQ, c_?NumericQ] := a + b + c

f1 @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}
(* {6, f[x, y, z], f[1, y, z], f[x, 2, z], f[x, y, 3]} *)

However, for functions with more than 1 variables, I'm way too lazy to add NumericQ after each parameter. Using /; at the end of the function definition works, but I feel it's still too long and I have to retype the name of the parameters (a,b,c) at the end.

Clear[f2, f3]
f2[a_, b_, c_] := a + b + c /; And @@ (NumericQ[#] & /@ {a, b, c})
f3[a_, b_, c_] := a + b + c /; VectorQ[{a, b, c}, NumericQ]

Is there any way to express the condition only once, and without having to type the list of parameters one more time? I know that this is a frivolous question borne out of sheer laziness but I'd love to hear your ideas.

(1) such as using the double underscore (BlankSequence) to apply NumericQ to any number of arguments passed to Plus (per Kuba's helpful suggestion). This is because these arguments have identical hierarchy in the function--thus having no need for parameters with different names to represent them--and because Plus can take any number of arguments.

Clear[f4]
f[a__?NumericQ] := Plus[a]
 
f @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}    
(* {6,f[x,y,z],f[1,y,z],f[x,2,z],f[x,y,3]} *)

I have a simple function that is supposed to only accept numeric values (i.e. complex/real numbers and constant symbols e.g. Pi, E).

$$f(a,b,c)=a+b+c$$

Edit: I should have chosen a less simple function for this question as there might be approaches that will work for this simple function but not for functions in general (1-see end of question). Please think of a more complicated function, such as $$f(a,b,c)=a^2 \sin(b) \log(c)$$ when you're thinking of an answer.

I know that one can use _?NumericQ for each parameter such that only numeric values of that parameters are entered into the function (click here for more information on putting constrains on patterns).

Clear[f1]
f1[a_?NumericQ, b_?NumericQ, c_?NumericQ] := a + b + c

f1 @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}
(* {6, f[x, y, z], f[1, y, z], f[x, 2, z], f[x, y, 3]} *)

However, for functions with more than 1 variables, I'm way too lazy to add NumericQ after each parameter. Using /; at the end of the function definition works, but I feel it's still too long and I have to retype the name of the parameters (a,b,c) at the end.

Clear[f2, f3]
f2[a_, b_, c_] := a + b + c /; And @@ (NumericQ[#] & /@ {a, b, c})
f3[a_, b_, c_] := a + b + c /; VectorQ[{a, b, c}, NumericQ]

Is there any way to express the condition only once, and without having to type the list of parameters one more time? I know that this is a frivolous question borne out of sheer laziness but I'd love to hear your ideas.

(1) such as using the double underscore (BlankSequence) to apply NumericQ to any number of arguments passed to Plus (per Kuba's helpful suggestion). This is because these arguments have identical hierarchy in the function--thus having no need for parameters with different names to represent them--and because Plus can take any number of arguments.

Clear[f4]
f[a__?NumericQ] := Plus[a]
 
f @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}    
(* {6,f[x,y,z],f[1,y,z],f[x,2,z],f[x,y,3]} *)

deleted 541 characters in body

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edited Aug 17, 2014 at 6:48

khanhnguyendata

5.2k
1
23
33

Clear[f]
(* Define function *)Clear[f1]
f[a_f1[a_?NumericQ, b_?NumericQ, c_?NumericQ] := a + b + c

(* Test function *)
ff1 @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}
(* {6, f[x, y, z], f[1, y, z], f[x, 2, z], f[x, y, 3]} *)

Mathematica graphics

Clear[f]
(* Define functionClear[f2, *)f3]
f[a_f2[a_, b_, c_] := a + b + c /; And @@ (NumericQ[#] & /@ {a, b, c})
 
(* Test function *)
f @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}

Mathematica graphics

Clear[f]
(* Define function *)
f[a_f3[a_, b_, c_] := a + b + c /; VectorQ[{a, b, c}, NumericQ]
 
(* Test function *)
f @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}

Mathematica graphics

Clear[f]
(* Define function *)Clear[f4]
f[a__?NumericQ] := Plus[a]
 
(* Test function *)
f @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}
     
(* {6,f[x,y,z],f[1,y,z],f[x,2,z],f[x,y,3]} *)

Mathematica graphics

Clear[f]
(* Define function *)
f[a_?NumericQ, b_?NumericQ, c_?NumericQ] := a + b + c

(* Test function *)
f @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}

Mathematica graphics

Clear[f]
(* Define function *)
f[a_, b_, c_] := a + b + c /; And @@ (NumericQ[#] & /@ {a, b, c})
 
(* Test function *)
f @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}

Mathematica graphics

Clear[f]
(* Define function *)
f[a_, b_, c_] := a + b + c /; VectorQ[{a, b, c}, NumericQ]
 
(* Test function *)
f @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}

Mathematica graphics

Clear[f]
(* Define function *)
f[a__?NumericQ] := Plus[a]
 
(* Test function *)
f @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}
 
(* {6,f[x,y,z],f[1,y,z],f[x,2,z],f[x,y,3]} *)

Mathematica graphics

Clear[f1]
f1[a_?NumericQ, b_?NumericQ, c_?NumericQ] := a + b + c

f1 @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}
(* {6, f[x, y, z], f[1, y, z], f[x, 2, z], f[x, y, 3]} *)

Clear[f2, f3]
f2[a_, b_, c_] := a + b + c /; And @@ (NumericQ[#] & /@ {a, b, c})
f3[a_, b_, c_] := a + b + c /; VectorQ[{a, b, c}, NumericQ]

Clear[f4]
f[a__?NumericQ] := Plus[a]
 
f @@@ {{1, 2, 3}, {x, y, z}, {1, y, z}, {x, 2, z}, {x, y, 3}}    
(* {6,f[x,y,z],f[1,y,z],f[x,2,z],f[x,y,3]} *)