I am writing a scientific report. Lets say there is an equation,
c = a+b where, a is variable1 b is variable2
Is it needed to put comma after "where" here? Also at the end of the equation, is a comma required?
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Speaking as someone in the mathematical sciences: I would strongly prefer a colon after where, as follows:
c = a+b,
a is quizzical,
b is mysterious
The punctuation I've used above is the same as what I would use in a written English sentence — albeit with a little bit of a telegraphic style (omitting the word 'and' after 'quizzical'). Alternatively, you can write it inline, in which case you should write it as though it were simple prose:
c = a+b, where a is quizzical and b is mysterious.
Instead of scientific writing, the question actually seems to be concerned with mathematical style guidelines for writing equations. The punctuation for the equation in your example is dependent on the context; mainly what precedes it. I would suggest styling the text differently for the equation (italics, perhaps). However, to answer your main question, no. It is a convention to add the comma before "where", or directly after the equation. Not after "where".
c = a+b, where a is variable1 and b is variable2
The "and" (and/or commas if you have more than two) is optional. In this situation, people aren't that worried about the punctuation. They care more about the formatting that gets the point across.