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Domen
Domen
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Suppose I have an expression which is a collection of symbols and integers arbitrarily combined with Plus and Times. For example, A = a + c (d - a b d) + e c (a + b) f + b - 1 or maybe B = a + b a c d 

A = a + c (d - a b d) + e c (a + b) f + b - 1

B = a + b a c d

(where a, b, c, d, e, f are all different symbols), although it could be longer and more complicated. 

I want to estimate the expression by reducing it to only the terms with zero or one symbol multiplied together because the symbols all represent small numbers, and I want a first-order approximation. E.g. Reduced A would be Ar = a+b-1 and reduced B is Br = a.:

Ar = a + b - 1

Br = a

How can I automate this in Mathematica? Assume that any constants are stand-alone and don't have to be distributed.

Suppose I have an expression which is a collection of symbols and integers arbitrarily combined with Plus and Times. For example, A = a + c (d - a b d) + e c (a + b) f + b - 1 or maybe B = a + b a c d (where a, b, c, d, e, f are all different symbols), although it could be longer and more complicated. I want to estimate the expression by reducing it to only the terms with zero or one symbol multiplied together because the symbols all represent small numbers, and I want a first-order approximation. E.g. Reduced A would be Ar = a+b-1 and reduced B is Br = a. How can I automate this in Mathematica? Assume that any constants are stand-alone and don't have to be distributed.

Suppose I have an expression which is a collection of symbols and integers arbitrarily combined with Plus and Times. For example,

A = a + c (d - a b d) + e c (a + b) f + b - 1

B = a + b a c d

(where a, b, c, d, e, f are all different symbols), although it could be longer and more complicated. 

I want to estimate the expression by reducing it to only the terms with zero or one symbol multiplied together because the symbols all represent small numbers, and I want a first-order approximation:

Ar = a + b - 1

Br = a

How can I automate this in Mathematica? Assume that any constants are stand-alone and don't have to be distributed.

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Gilbert
Gilbert
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Suppose I have an expression which is a collection of symbols and integers arbitrarily combined with Plus and Times. For example, $A = a+c(d - a b d)+e c(a+b)f+b-1$A = a + c (d - a b d) + e c (a + b) f + b - 1 or maybe $B = a + bacd$B = a + b a c d (where $a$a, $b$b, $c$c, $d$d, $e$e, $f$f are all different symbols), although it could be longer and more complicated. I want to estimate the expression by reducing it to only the terms with zero or one symbol multiplied together because the symbols all represent small numbers, and I want a first-order approximation. E.g. Reduced A would be $A \to a+b-1$Ar = a+b-1 and reduced B is $B \to a$Br = a. How can I automate this in Mathematica? Assume that any constants are stand-alone and don't have to be distributed.

Suppose I have an expression which is a collection of symbols and integers arbitrarily combined with Plus and Times. For example, $A = a+c(d - a b d)+e c(a+b)f+b-1$ or maybe $B = a + bacd$ (where $a$, $b$, $c$, $d$, $e$, $f$ are all different symbols), although it could be longer and more complicated. I want to estimate the expression by reducing it to only the terms with zero or one symbol multiplied together because the symbols all represent small numbers, and I want a first-order approximation. E.g. $A \to a+b-1$ and $B \to a$. How can I automate this in Mathematica? Assume that any constants are stand-alone and don't have to be distributed.

Suppose I have an expression which is a collection of symbols and integers arbitrarily combined with Plus and Times. For example, A = a + c (d - a b d) + e c (a + b) f + b - 1 or maybe B = a + b a c d (where a, b, c, d, e, f are all different symbols), although it could be longer and more complicated. I want to estimate the expression by reducing it to only the terms with zero or one symbol multiplied together because the symbols all represent small numbers, and I want a first-order approximation. E.g. Reduced A would be Ar = a+b-1 and reduced B is Br = a. How can I automate this in Mathematica? Assume that any constants are stand-alone and don't have to be distributed.

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Gilbert
Gilbert
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  • 5

Reducing a symbolic expression to only its lowest-order terms

Suppose I have an expression which is a collection of symbols and integers arbitrarily combined with Plus and Times. For example, $A = a+c(d - a b d)+e c(a+b)f+b-1$ or maybe $B = a + bacd$ (where $a$, $b$, $c$, $d$, $e$, $f$ are all different symbols), although it could be longer and more complicated. I want to estimate the expression by reducing it to only the terms with zero or one symbol multiplied together because the symbols all represent small numbers, and I want a first-order approximation. E.g. $A \to a+b-1$ and $B \to a$. How can I automate this in Mathematica? Assume that any constants are stand-alone and don't have to be distributed.