View Single Post
Old 03-01-2022, 10:19 AM   #47
Turtle91
A Hairy Wizard
Turtle91 ought to be getting tired of karma fortunes by now.Turtle91 ought to be getting tired of karma fortunes by now.Turtle91 ought to be getting tired of karma fortunes by now.Turtle91 ought to be getting tired of karma fortunes by now.Turtle91 ought to be getting tired of karma fortunes by now.Turtle91 ought to be getting tired of karma fortunes by now.Turtle91 ought to be getting tired of karma fortunes by now.Turtle91 ought to be getting tired of karma fortunes by now.Turtle91 ought to be getting tired of karma fortunes by now.Turtle91 ought to be getting tired of karma fortunes by now.Turtle91 ought to be getting tired of karma fortunes by now.
 
Turtle91's Avatar
 
Posts: 3,361
Karma: 20212223
Join Date: Dec 2012
Location: Charleston, SC today
Device: iPhone 15/11/X/6/iPad 1,2,Air & Air Pro/Surface Pro/Kindle PW & Fire
Quote:
Originally Posted by salamanderjuice View Post
Considerably smaller. Let's use the Taylor series expansion as an example.

In LaTeX this can be written as:
Code:
f(x)=\sum_{k=0}^\infty f^{(k)}(a)\frac{(x-a)^k}{k!}
This is 51 characters total. The MathML version is a little more verbose at 867 characters:
Code:
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>x</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mo accent="false">∞</mo></munderover><msup><mi>f</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>k</mi><mo stretchy="true" form="postfix">)</mo></mrow></msup><mrow><mo stretchy="true" form="prefix">(</mo><mi>a</mi><mo stretchy="true" form="postfix">)</mo></mrow><mfrac><msup><mrow><mo stretchy="true" form="prefix">(</mo><mi>x</mi><mo>−</mo><mi>a</mi><mo stretchy="true" form="postfix">)</mo></mrow><mi>k</mi></msup><mrow><mi>k</mi><mi>!</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">f(x)=\sum_{k=0}^\infty f^{(k)}(a)\frac{(x-a)^k}{k!}</annotation></semantics></math><
But it's trying to be unambiguous. The SVG version is 28621 characters which I'm not going to put here.

Assuming 1 character is 1 byte which isn't quite accurate the LaTeX version 0.05KB, the MathML version is 0.85KB and the SVG version is 27.95KB. And the PNG version I made that's tolerable is 1.3KB.
That is quite a bit of difference!!

Thanks for the info!
Turtle91 is offline   Reply With Quote