Is there a way to solve partial fractions on mathematica, other than ‘apart’ function. Maybe an add on function?

# Tag: function

## Invalid Function after Spatial remove

I Removed Spatial (SDO) from my Oracle 19c CDB and now i got a Invalid function called:

NDM_RESET_ID_GENERATOR FUNCTION MDSYS

Does someone know how to fix it?

## What function can I use to determine new user registration?

I have created a function that sends a message to members. I would like this function to fire **only** if the user has just registered.

`function send_message_to_new_member() { // If user has just created account if( is_new_user() ) { //is_new_user() doesn't exist, so how can I go about this? // Do something } } add_action( 'woocommerce_order_status_completed', 'send_message_to_new_member', 2 ); `

Registration will take place at the Woocommerce checkout… not sure is the method of registration is different there compared to standard WordPress registration?

## How to create a postgres function that returns a value

I am trying to move some of my web app logic into postgres functions. But I am hitting some errors while creating a very basic insert function.

This is the function that I am trying to create;

`CREATE OR REPLACE FUNCTION create_user(IN email EMAIL, password TEXT, thumb TEXT) RETURNS text AS $ BODY$ BEGIN insert into users (unqid, thumb, email, password) values (gen_random_uuid(), thumb, email, password) returning unqid ; END; $ BODY$ LANGUAGE plpgsql VOLATILE `

I am trying to get the function to return the uuid of the item if the insert is successful. And I am calling it like this;

`select * from create_user('newuser@mail.com', 'passpopcorn', 'thumbelinaurl'); `

Getting this error;

`SQL Error [42601]: ERROR: query has no destination for result data Where: PL/pgSQL function create_user(email,text,text) line 3 at SQL statement `

From my googling it sounds like this error comes up when you don’t have a return statement in the query. But in my Insert query, I do have a returning statement.

Extra question; for simple insert statements (like this one here, or one with a couple of select followed by an insert), would functions be a better bet or procedures?

## “Total” function for a Boolean expression

I have a very long vector of the form

`{a1 a2 a3 a4 + b1 b2 b3 b4 + c1 c2 c3 c4 + d1 d2 d3 d4 + e1 e2 e3 e4, a1 a2 a3 a4 + b1 b2 b3 b4 + c1 c2 c3 c4 + d1 d2 d3 d4 + e1 e2 e3 e4, a1 a2 a3 a4 + b1 b2 b3 b4 + c1 c2 c3 c4 + d1 d2 d3 d4 + e1 e2 e3 e4, ...} `

(here I just repeated the elements for simplicity, but in general, each element is different). And I want to transform it into a Boolean expression where `Plus->Or`

and `Times->And`

.

What is the fastest way to do it? At the moment, I use `Replace`

, but it’s really slow when the expression is bigger. Here the simpler example takes 0.000034 seconds:

`RepeatedTiming[{a1 a2 a3 a4 + b1 b2 b3 b4 + c1 c2 c3 c4 + d1 d2 d3 d4 + e1 e2 e3 e4, a1 a2 a3 a4 + b1 b2 b3 b4 + c1 c2 c3 c4 + d1 d2 d3 d4 + e1 e2 e3 e4, a1 a2 a3 a4 + b1 b2 b3 b4 + c1 c2 c3 c4 + d1 d2 d3 d4 + e1 e2 e3 e4} /. {Times -> And} /. {Plus -> Or}] `

Also, is there an equivalent of the `Total`

function for Boolean expressions?

## How to reconstruct a complicated built-in function (e.g. for modification or use in a version that does not have it yet)

Is it possible to extract the definitions for a built-in function to reconstruct a similar user defined function. This would be useful to port new mathematica functionality to older versions or to create modified versions of built-in functions.

I found that

`Needs["GeneralUtilities`"] PrintDefinitions[symbol]; `

could get us close (see https://mathematica.stackexchange.com/a/78898/45020) but it would still be quite a job to reconstruct the full function including all of its dependencies from there. Have there been any automated attempts to try this kind of thing?

As an example I would be very interesting in reconstructing `ExternalEvaluate`

(or if that is too ambitious to reconstruct only the part that converts Mathematica arguments supplied with `"Arguments"->{args}`

to python expressions in the case that we `ExternalEvaluate`

using a python session.)

(I hope this type of question is not frowned upon in light of copyright issues. I would just like to deal with incompatibility issues between different (Licensed) versions of Mathematica.)

## OptionValue doesn’t work if a local variable has the same name as the function itself

The following innocent-looking code results in error.

`Options[add] = {number -> 1}; add[x_, OptionsPattern[]] := Module[{add}, x + OptionValue[number] ]; add[1] `

The error is

`OptionValue::optnf: Option name number not found in defaults for add$ 2832. `

What triggers the error is the fact that a local variable declared by `Module`

has the same name as the function, `add`

. (For simplicity, I’ve shown an example where this local variable isn’t actually used in the code, but this doesn’t make a difference.)

Is this a bug in Mathematica, or some known quirk of OptionValue[]?

## PostgreSQL backend function after an elog(ERROR) had been issued

Getting this weird issue one time per postgresSql session. Like if I run this query first time, will return with below message but if I rerun the same, it works fine.

DEBUG: An attempt was made to call a PostgreSQL backend function after an elog(ERROR) had been issued ERROR: org.glassfish.jersey.internal.ServiceConfigurationError: org.glassfish.jersey.internal.inject.InjectionManagerFactory: : java.io.IOException: An attempt was made to call a PostgreSQL backend function after an elog(ERROR) had been issued.

## WordPress: Call to undefined function wp_embed_register_handler()

I have a WordPress website that is still under development. I was working on this website till end of Feb, 2021 and hold all works due to COVID crises. Till that date, website was working. Now I have resumed my work and just looking into website. But now, website is throwing an error "**Fatal error: Uncaught Error: Call to undefined function wp_embed_register_handler()**"

I have also crossed the file "wp-includes/embed.php" file in which this function exists and function is already defined before calling it. You can see attached screenshot of whole error tracing.

I am not getting this error on all pages but almost every pages. I am not able to understand why I am getting this error even I have not touched anything on website from last 3-4 months. And it was working fine when I was working last.

Can someone please help on this? I am not very experienced in WordPress but have intermediate knowledge.

Thanks in Advance

## Parametric plot of a function which cannot be explicitly calculated

I wish to plot a function, but I run into a problem and I cannot find similar questions here. A simplified version of plot is represented by

ParametricPlot[{g,f[x,y]}, {x,a,b},{y,c,d}]

f is quite a tricky expression and cannot be explicitly calculated for unknown x and y. Hence this plot does not work, as I believe Mathematica first explicitly calculates f[x,y] and then thereafter substitutes x and y in order to plot this. However, how can I do this such that f[x,y] substitutes the explicit values for x and y into f, as then the function can be calculated? For example, f[1,2] works absolutely fine, f[x,y] is the problem.

edit:

My code:

` cc = 0.4; cD = 0.1; r = 10.2; Nstar = Floor[r]; rhos1[N_] := (1 - N/r)*Lambda^N* Exp[eps]*Delta; rhos2[N_] := (1 - N/r)*(Lambda*Exp[g])^N* Exp[eps]*Delta*Exp[g*Nstar] rho = Sum[rhos1[n], {n, 1, Nstar}] + Sum[rhos2[n], {n, Nstar + 1, Infinity}]; phi = Sum[n*rhos1[n], {n, 1, Nstar}] + Sum[n*rhos2[n], {n, Nstar + 1, Infinity}]; phi3[Delta_] := Sum[n*(1 - n/r)*\[CapitalLambda]^n* Exp[\[Epsilon]]*Delta, {n, 1, Nstar}] + Sum[n*(1 - n/r)*(Lambda*Exp[g])^n* Exp[eps]*Delta*Exp[g*Nstar], {n, Nstar + 1, Infinity}]; RhoDivided3 = Simplify[rho/Delta] h1 = cD/(RhoDivided3 + Exp[g]); f[eps1_, g1_] := Apply[List, Reduce[cc == ReplaceAll[phi3[h1] + Lambda* Exp[eps], {eps -> eps1, g -> g1}] && Lambda > 0 && Lambda < 0.99999, Lambda], {0, 1}][[2]] Plot[ReplaceAll[phi/rho, {Lambda -> f[-2, g], eps -> -2}], {g, -30, -10}] `

Therefore f is obtained by solving a very complex equation for Lambda, and so cannot be determined as a function of epsilon and g, as explicit values are required.