diman.attach — com.neuralgraphs/diman 1.0.4

Contains function. These are:

• tie-notn-expt
• tie-subformula-expt
• tie-notnlist-exptlist
• tie-ref-with-distinct-next
• tie-subformulae-in-term
• tie-subformulae-in-eqn-side
• tie-names-in-subformula

How to use

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(:require [diman.attach :refer :all])

Examples

Attaching an exponent to one of seven fundamental notations

For notation [M] with exponent 2

=> (tie-notn-expt "[M]" "2")
"M^(2)"

which is a formula with just one component, M^(2).

Attach exponent of a variable/parameter in the expression

Consider the expression v^2 where variable/parameter v stands for velocity with the standard formula [M^(0)*L^(1)*T^(-1)]. To attach the exponent (= 2) of v to its standard formula is to multiply all the exponents of the notations contained in the standard formula

=> (tie-subformula-expt "[M^(0)*L^(1)*T^(-1)]" "2")
"[M^(0.0)*L^(2.0)*T^(-2.0)]"

NOTE:

• tie-subformula-expt is for all practical purpose multiplying exponents of all the notations in the formula by the desired exponent value.
• it is similar to allexpt-times-expt in diman.exponents but unlike it tie-subformula-expt returns the same form of the formula (say, standard formula) but with exponents changed while allexpt-times-expt only returns the list of changed exponents.

Attach list of notation and its corresponding list of exponents

For a list [("M" "L" "T") ("0" "1" "-2")] defined in x its formula is

=> (tie-notnlist-exptlist x)
"[M^(0)*L^(1)*T^(-2)]"

NOTE:

• the list of notation and its exponents is usually that of a sub-formula, that is, formula of variable/parameter in a term comprised of >= variable/parameter
• the list can be obtained using the list-varpar-expt (in diman.filter namespace)
• for a list of sub-formulae = lform = [form1 form2 from3 ...] to get the list of notation and exponents of form1 you get x from (list-varpar-expt (remove-brackets (first lform)))

Attach distinct components in next sub-formula to the reference sub-formula

Given an expression (lhs or rhs of the equation), let us assume that a variable/parameter for the defined problem has a formula representation. An expression is composed of subexpressions separated by + sign. We shall refer to each subexpression as a term.

As a general convention formula for each term is referred here as a sub-formula. The sub-formula will be the result of the term regardless of the number of variable/parameter. A sub-formula consists of components which themselves are made up of the base notations. The number of components in a sub-formula resulting from a term with one variable/parameter will be the number of base notations in the sub-formula.

However, if the sub-formula is a result of a term with more than one variable/parameter then each formula resulting from respective variable/parameter is referred to as the supra-component. A supra-component consists of components made up of base notations.

A term with one variable/parameter will have only one supra-component or sub-formula (dimensional formula of the variable/parameter). A term with n variable/parameters will have n supra-components in one sub-formula. In such cases, the sub-formula of the term is the union of supra-components.

For the example of the term whose list of sub-formulae is (def lform '("[M^(0)*L^(1)*T^(-2)]" "[A^(1)*T^(2)]" "[cd]^(0)*[mol]^(-2)]")) "[M^(0)*L^(1)*T^(-2)]" is taken as the reference sub-formula because it is the longest. Looking at "[A^(1)*T^(2)]" the notation common with the reference is T so

=> (tie-ref-with-distinct-next (first lform) (second lform) "[T^(2)]")
"[T^(-2)*M^(0)*L^(1)*A^(1)]"

Considering "[cd]^(0)*[mol]^(-2)]" since there are nil notations in common with the reference

=> (tie-ref-with-distinct-next (first lform) (last lform) nil)
"[T^(-2)*mol^(-2)*M^(0)*cd^(0)*L^(1)]"

Also notice that tying with itself (reference subformula) will return itself

=> (tie-ref-with-distinct-next (first lform1) (first lform1) nil)
"[T^(-2)*M^(0)*L^(1)]"

Therefore, this function returns a sub-formula comprising all the distinct components among the sub-formulae resulting from the variable/parameter.

Tying the sub-formulae of a term to get the term formula

The sub-formulae of a term or expression will normally have notations and hence components that are in common to the sub-formulae generated from the variable/parameter defined in the expression. Therefore, to obtain the sub-formula of a term or an expression comprised of just one term the first step is to create a sub-formula composed of distinct components.

Given the list of sub-formulae defined above

=> lform
("[M^(0)*L^(1)*T^(-2)]" "[A^(1)*T^(2)]" "[cd]^(0)*[mol]^(-2)]")

with the reference sub-formula "[M^(0)*L^(1)*T^(-2)]", notice that there are other sub-formula in the list that have components with same notation as in the reference sub-formula. Here, it is T^(2). Also, although it is represented as a list the sub-formulae have the multiplication operator between them. With this knowledge and the law of exponents the updated reference sub-formula is

"[M^(0)*L^(1)*T^(0)]"

Then the formula of the term is its tied sub-formulae

=> (tie-subformulae-in-term lform "[M^(0)*L^(1)*T^(0)]")
"[mol^(-2)*T^(0)*M^(0)*cd^(0)*L^(1)*A^(1)]"

Notice that this function ties up the updated reference sub-formula with distinct components in the rest of the sub-formulae; note distinct relative to the reference.

Tying the sub-formulae of an equation side to get its formula

In the context of formula for a side of the equation the formulae of each of term are its sub-formulae. These then can be tied up using tie-subformulae-in-eqn-side.

Therefore, if the right hand side of the equation is

(def rhs {:term1 "x^(1)", :term2 "v^(2)", :term3 "t^(1)", :term4 "0.5*a^(1)*t^(2)"})

resulting in its corresponding sub-formulae

("[L^(1)]" "[T^(-2)*M^(0)*L^(2)]" "[T^(1)]" "[T^(0)*M^(0)*L^(1)]")

Then when tied up we get

=> (tie-subformulae-in-eqn-side '("[L^(1)]" "[T^(-2)*M^(0)*L^(2)]" "[T^(1)]" "[T^(0)*M^(0)*L^(1)]"))
"[L^(1)] + [T^(-2)*M^(0)*L^(2)] + [T^(1)] + [T^(0)*M^(0)*L^(1)]"

NOTE: Unlike tying of sub-formulae for getting the term formula, sub-formulae tying for the equation side does not perform exponent operation. This is because for the case of equation side the sub-formulae are separated by the addition operator.

Tying dimension names in a sub-formula

To have a more readable view of the sub-formula of the term

=> (tie-subformulae-in-term lform "[M^(0)*L^(1)*T^(0)]")
"[mol^(-2)*T^(0)*M^(0)*cd^(0)*L^(1)*A^(1)]"

you can call tie-names-in-subformula as

=> (tie-names-in-subformula "[mol^(-2)*T^(0)*M^(0)*cd^(0)*L^(1)*A^(1)]")
"amount of substance^(-2)*length^(1)*electric current^(1)"

Notice that names of the dimensions with exponent value = 0 is not shown. If it were it would have appeared as

"amount of substance^(-2)*time^(0)*mass^(0)*luminous intensity^(0)*length^(1)*electric current^(1)"

tie-names-in-subformula clj

(tie-names-in-subformula subform)

(tie-names-in-subformula subform lst_names lst_expts tied_name_expts)

Returns dimension name and its exponent value with each pair separated by *.

tie-notn-expt clj

(tie-notn-expt notn expt)

tie-notnlist-exptlist clj

(tie-notnlist-exptlist lst_notn_expt)

(tie-notnlist-exptlist lst_notn_expt lst_notn lst_expt notn_expt_joined)

Returns sub-formula by tying the list of notations with its corresponding list of exponents.

tie-ref-with-distinct-next clj

(tie-ref-with-distinct-next ref_subform next_subform common)

tie-subformula-expt clj

(tie-subformula-expt subform varpar_expt)

(tie-subformula-expt lst_notn lst_expt lst_comps)

Returns sub-formula attached to the multiplied exponents, multiplied by a given exponent.

tie-subformulae-in-eqn-side clj

(tie-subformulae-in-eqn-side lst_formulae)

tie-subformulae-in-term clj

(tie-subformulae-in-term lst_subform updated_ref_subform)

(tie-subformulae-in-term lst_subform updated_ref_subform updated_ref_tied)

Returns formula of the terms by tying up sub-formulae. Specifically, tying the updated reference sub-formula with distinct components in rest of sub-formulae.