path: root/2025/captions/emacsconf-2025-calc--basic-calc-functionality-for-engineering-or-electronics--christopher-howard--main.vtt

WEBVTT captioned by sachac

NOTE Introduction

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Hello, my name is Christopher Howard and welcome to my talk.

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This is basically an introduction

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to the built-in Emacs calculator,

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properly known as Emacs Calc,

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particularly from the perspective of someone

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with a technical background such as engineering or electronics.

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I will say, though, my personal interest is not really

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in digital computing or digital calculators,

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but lately has been focused more on analog computing.

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I have, for example, been working to master

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the venerable slide rule, a mechanical computer

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that calculates multiplication powers and logarithms.

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Here's a picture of one.

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It's a physical tool that was used for hundreds of years

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for this sort of thing

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before the handheld calculator was made popular.

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And I also had a project that I did

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for a while to several months

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to build an electronic analog computer.

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A rudimentary attempt of mine, but it's functional,

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and it's basically a 1960s or 1970s style

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electronic analog computer built very much on a budget,

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but the box in the middle is the computer proper

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which has most of the components inside of it

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as well as the potentiometers for setting values,

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and an operation switch.

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There's a patch panel on the left

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for connecting the different integrators,

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amplifiers, multipliers, and so forth together.

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Then the output of the simulation is displayed

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on the oscilloscope on the right side,

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which is a digital oscilloscope.

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To be honest, I think that a talk about analog computing

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would be much more interesting

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than the talk that I'm about to give,

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but unfortunately that would be out of scope for EmacsConf.

NOTE What is Calc?

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So instead I will talk about Emacs Calc,

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the digital calculator built into Emacs.

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Emacs Calc, while not being a replacement for software

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like GNU Octave, does have advanced calculator functionality

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that can be useful in engineering, electronics,

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or other technical applications. So I don't want to oversell it,

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but I think functionality-wise, Calc is somewhere in between

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what you'd expect of a decent scientific calculator

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and an advanced graphics calculator.

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So this talk I'll mention is not intended to be a tutorial

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but only a brief introduction to Calc.

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Please refer to the built-in Calc info manual

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for detailed instructions on how to complete operations.

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Turn off my volume here.

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The documentation for Emacs Calc is built-in,

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although on some distributions you may have to install

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the Emacs documentation separately for licensing reasons.

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Calc presents itself as a stack-based calculator

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where entries are dropped onto a stack

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and then an operation is performed on the stack entries.

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For example, I can drop 1.23 onto the stack,

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and then 8.56, and then multiply them together.

NOTE calc-algebraic-entry

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It may present itself as a stack-based calculator,

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but indeed, Calc is also capable of accepting input

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in the more well-known algebraic format

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by using the calc-algebraic-entry command,

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which by default is bound to the apostrophe (') key.

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So you type the apostrophe key, enter the algebraic input,

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including parentheses as needed.

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For example, here's a calculation of the resonance frequency

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of a coil which has an inductance of 250 microhenries

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and 160 picofarads, taken from one of my electronics handbooks.

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The formula for that is 1 over 2 pi

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and then the square root of our inductance

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which is in this case 250 microfarads - excuse me, microhenries

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and then the capacitance is 160 picofarads.

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Small typo here.

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Now I need to evaluate that one more time,

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because pi is a symbol.

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I get about 800 kHz resonant frequency.

NOTE calc-roll-down

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The command calc-roll-down,

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which by default is bound to the TAB key,

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will swap the top two stack entries,

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which is sometimes useful if you need to manipulate something

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that's further down the stack.

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So I can swap this around and say multiply by two

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and then put it back where it was.

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This command is also capable of rolling the entire stack.

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Say I want to shift them all around.

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This can be done by passing extra arguments

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to the calc-roll-down function.

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That's a little bit inconvenient to do manually,

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so in my init file, I defined here a key definition

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that passes in those arguments correctly.

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I attached this to shift-tab,

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so this way, I can roll the entire stack.

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Then I could change one entry here

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and then put it back where it was.

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So Calc does algebraic input.

NOTE Advanced functions

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It also does advanced functions

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that you would expect any handheld scientific calculator,

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including trigonometric functions.

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For example, we can get the sine of a number.

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Now I'll mention here that Calc has multiple modes.

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Right now it's in degree mode.

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You can switch over to radian mode if you want.

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I'm going to put it back in degrees.

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Drop 12 degrees on the stack, and then get the sine of that.

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And then with the inverse sine function, I can put it back.

NOTE Solving equations with calc-solve-for

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Calc also has the nifty ability to solve equations for you

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so long as the equation is not too complicated.

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This is using the calc-solve-for function.

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For example, we could enter in an equation algebraically,

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then run calc-solve-for, and we just have to tell it

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what variable we want to solve for. And there we go.

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We can do this manually as well

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just so you can see that we get the same result.

NOTE Systems of equations

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Calc is also able to solve systems of equations.

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We can put more than one equation on the stack,

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and then solve for several variables.

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To give a technical example for this,

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I'll show you a resistor network scribble that I did recently.

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Hopefully you can see that. Basically,

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it's fairly simple, a pretty simple resistor network

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with 1 kilo ohm and 10 kilo ohm resistors,

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and using the loop methods, we are calculating the currents,

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the current in each loop, and then that current can be used

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to solve for the voltage of each individual resistor

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if we want to. So at the bottom there we have the equations

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that we come up with as we work through each loop.

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And I'm going to paste that into Calc.

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To save some time, I'm going to copy and paste that

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from my notes instead of typing it out.

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So we have two equations there on the stack

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in one stack entry. We run that calc-solve-for function again,

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and we tell it which variables we want to solve for.

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And voila! Those are our currents,

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which we can then use to get the voltages

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for the individual resistors.

NOTE calc-find-root

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I'll just briefly mention

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that if Calc is not able to solve an equation

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with calc-solve-for,

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then you might be helped by another calc function

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called calc-find-root.

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This function basically does a manual search

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for a numerical solution to the equation.

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And there's the documentation page on that.

NOTE Derivatives and integrals

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Calc can also solve or find derivatives of functions,

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at least the more straightforward functions.

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For a simple example,

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we can get the derivative of that

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with the derivative function.

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On the other hand, Calc is also capable of figuring out

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indefinite integrals.

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Say we put that function back on the stack,

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and this time, we call the integral function.

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There you go. Of course, you have to add

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your own constant of integration.

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For integrals that Calc cannot figure out symbolically,

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a numerical integration method is available

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through the calc-num-integral command, which is documented...

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The function  documentation is available here, more or less.

NOTE Programmable functions

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I definitely need to mention

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that Calc is capable of doing programmable functions.

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That is to say, you can program your own functions into Calc.

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There are three separate ways to do this.

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One is through a macro method

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similar to Emacs's usual keyboard macros.

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The second method is to transform an algebraic function

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into a stored function definition.

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And the third is to use Elisp directly.

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Personally, I find that the second method

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is the most practical, the most convenient and practical

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in my opinion. So I'll give a quick example of that.

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So I could... Let's say I wanted to have a function

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for calculating capacitive reactance.

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I'll define that in algebraic mode first.

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The function for that is 1 over 2 pi

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the frequency and the capacitance.

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Drop that on the stack. You see, it does automatically

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get simplified a little bit, but it's the same function.

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And then I press letters Z and F. Do that again.

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Z and F to start transforming that into a stored function.

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It asks me to select a user key, a single key press.

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I'll use the letter c.

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Then it's going to ask for a longer command name.

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I've actually defined this once before, so it prefilled in

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that command name.

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Then I need to enter which variables in the formula

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are actual arguments, rather than just symbols

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to be evaluated later. I prefer to put this in with frequency

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and the capacitance after that,

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but actually in this particular case,

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it doesn't matter at all to the mathematics.

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So, now all I have to do, that this is defined,

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is I can drop the frequency on the stack,

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which we'll say, for this example, will be 4.5 MHz,

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and then drop on the capacitance, which in this example

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will be 22 pF.

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Then I'll call the function that I just defined.

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I don't really like having to try to remember

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the short letters that I've come up with,

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so I'll just use the longer name.

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I need to evaluate one more time

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because the symbol pi is in there and not yet evaluated.

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And so if I've done that right,

00:18:07.540 --> 00:18:12.159
we have a capacitive reactance of about 1600 ohms.

NOTE Plotting

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As the last feature that I'll mention here,

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Emacs Calc does have an interface with gnuplot,

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if you want to have Calc work as your graphing calculator.

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I do need to be honest and mention

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that I don't generally use it myself

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because there's another program in GNOME

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that I've found to be generally more convenient

00:18:43.500 --> 00:18:47.399
for the things that I want to graph quickly.

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But I think I can give you a simple example.

00:18:53.400 --> 00:19:00.339
So first, we need to drop a range on the stack.

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Let's say 0 to 10.

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And then we need to drop the function on the stack.

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And then I believe it's the letters g and f that graph this.

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Let's see. Yep, there we go.

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So there's our function and it looks nice.

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That was pretty easy.

00:19:26.660 --> 00:19:29.019
That's the fast way to do it.

00:19:29.020 --> 00:19:32.839
I will, as a disclaimer, mention that

00:19:32.840 --> 00:19:34.159
using this quick approach,

00:19:34.160 --> 00:19:38.759
that sometimes more complicated graphs

00:19:38.760 --> 00:19:39.999
will not turn out nicely,

00:19:40.000 --> 00:19:44.339
because by default, the resolution will be pretty low.

00:19:44.340 --> 00:19:48.119
That is to say it's... gnuplot is going to be

00:19:48.120 --> 00:19:49.899
skipping a lot of points

00:19:49.900 --> 00:19:52.039
and so you'll have to learn a bit more

00:19:52.040 --> 00:19:55.319
about how to use the interface,

00:19:55.320 --> 00:19:59.519
what parameters to pass if you want all your graphs

00:19:59.520 --> 00:20:03.699
to come out looking nice.

00:20:03.700 --> 00:20:08.799
So that covers all the features that I wanted to cover.

NOTE Wish list

00:20:08.800 --> 00:20:13.279
I wanted to briefly mention a wish list of items

00:20:13.280 --> 00:20:16.679
that I'd like to see in Calc.

00:20:16.680 --> 00:20:23.639
One of them would be improper integrals.

00:20:23.640 --> 00:20:25.159
So that's like our definite integrals

00:20:25.160 --> 00:20:32.859
except for where a limit of integration is infinity.

00:20:32.860 --> 00:20:38.559
That's something that can be useful in a few applications.

00:20:38.560 --> 00:20:41.079
Something else that would be neat to have would be

00:20:41.080 --> 00:20:45.679
annotations for row entries. So for example

00:20:45.680 --> 00:20:48.819
if I was putting together a sum of numbers

00:20:48.820 --> 00:20:53.279
for, say, my monthly budget,

00:20:53.280 --> 00:20:57.479
let's say I was paying $2,000 for my rent

00:20:57.480 --> 00:21:03.831
and let's say $800 a month for my groceries,

00:21:03.832 --> 00:21:07.931
(a lot of kids to feed there)

00:21:07.932 --> 00:21:14.565
and then say another $60 for dining out, and so on,

00:21:14.566 --> 00:21:18.259
it would be nice if there was some way

00:21:18.260 --> 00:21:21.319
to put a little annotation next to each number

00:21:21.320 --> 00:21:23.399
so that you could remember

00:21:23.400 --> 00:21:27.039
what the meaning of that number was more easily.

00:21:27.040 --> 00:21:31.199
I actually looked into programming this into Calc myself,

00:21:31.200 --> 00:21:35.919
but discovered that it would require reprogramming

00:21:35.920 --> 00:21:41.839
quite a bit of Calc to make that work well

00:21:41.840 --> 00:21:43.479
across all calc functionality,

00:21:43.480 --> 00:21:46.939
and so, eventually, I gave up.

00:21:46.940 --> 00:21:51.139
But I'd still really like to have that feature.

00:21:51.140 --> 00:21:52.039
The final thing, though

00:21:52.040 --> 00:21:54.579
I think this would not necessarily belong in Calc,

00:21:54.580 --> 00:21:57.919
I think it would be cool if Emacs had some way

00:21:57.920 --> 00:22:00.599
to run numerical solutions

00:22:00.600 --> 00:22:02.599
for systems of differential equations,

00:22:02.600 --> 00:22:06.019
also known as a differential analyzer.

00:22:06.020 --> 00:22:09.279
So this would allow you to be able to set up simulation models

00:22:09.280 --> 00:22:11.679
involving systems of differential equations,

00:22:11.680 --> 00:22:14.879
for example, a spring mass system, or pressure temperature,

00:22:14.880 --> 00:22:18.039
or what have you, and then run the simulation

00:22:18.040 --> 00:22:22.119
using numerical approximation.

00:22:22.120 --> 00:22:24.079
Maybe it would be silly

00:22:24.080 --> 00:22:25.999
to actually put that in Calc itself,

00:22:26.000 --> 00:22:30.339
but a nice interface maybe to some other software,

00:22:30.340 --> 00:22:33.299
simple software that did that,

00:22:33.300 --> 00:22:35.779
an easy to use interface for that

00:22:35.780 --> 00:22:38.599
would be really great.

NOTE Wrapping up

00:22:38.600 --> 00:22:41.800
So that's my entire talk.

00:22:41.801 --> 00:22:44.534
I'll just mention some information.

00:22:44.535 --> 00:22:48.365
If you want to learn more about me

00:22:48.366 --> 00:22:50.119
or things that I'm interested in,

00:22:50.120 --> 00:22:57.779
I do not any longer have a web presence.

00:22:57.780 --> 00:22:59.659
I don't have a website anymore,

00:22:59.660 --> 00:23:03.359
but I do have a Gemini capsule

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that I post to all the time.

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And if you can install, if you're willing to install the...

00:23:13.880 --> 00:23:19.079
Gemini browser known as Elpher

00:23:19.080 --> 00:23:23.698
into Emacs, which is available from ELPA,

00:23:23.699 --> 00:23:27.359
then you can browse directly to it

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and look around my Gemini capsule.

00:23:31.440 --> 00:23:35.920
Thank you very much.