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standard library package Quantities {
doc
/*
* This package defines the root representations for quantities and their values.
*/
private import Collections::*;
private import ScalarValues::NumericalValue;
private import ScalarValues::Number;
private import ScalarValues::Real;
private import ScalarValues::Natural;
private import ScalarValues::Boolean;
private import ScalarValues::String;
private import VectorValues::NumericalVectorValue;
private import VectorValues::ThreeVectorValue;
abstract attribute def TensorQuantityValue :> Array {
doc
/*
* The value of a quantity is a tuple of one or more numbers (i.e. mathematical number values) and a reference to a measurement reference.
* The most general case is a multi-dimensional, tensor quantity of any order. In engineering, the majority of quantities used are
* scalar and vector quantities, that are tensor quantities of order 0 and 1 respectively.
* The measurement reference used to express a quantity value must have a type, dimensions and order that match the quantity, i.e.,
* a TensorQuantityValue must use a TensorMeasurementReference, a VectorQuantityValue a VectorMeasurementReference,
* and a ScalarQuantityValue a ScalarMeasurementReference. See package MeasurementReferences for details.
*/
attribute isBound: Boolean;
attribute num: Number[1..*] ordered nonunique :>> elements;
attribute mRef: MeasurementReferences::TensorMeasurementReference;
attribute :>> dimensions = mRef.dimensions;
attribute order :>> rank;
attribute contravariantOrder: Natural;
attribute covariantOrder: Natural;
assert constraint orderSum { contravariantOrder + covariantOrder == order }
assert constraint boundMatch { (isBound == mRef.isBound) or (not isBound and mRef.isBound) }
}
abstract attribute def VectorQuantityValue :> TensorQuantityValue, NumericalVectorValue {
attribute :>> mRef: MeasurementReferences::VectorMeasurementReference;
}
abstract attribute def ScalarQuantityValue :> VectorQuantityValue, NumericalValue {
attribute :>> mRef: MeasurementReferences::ScalarMeasurementReference;
}
abstract attribute tensorQuantities: TensorQuantityValue[*] nonunique {
doc
/*
* Quantities are defined as self-standing features that can be used to consistently specify quantities as
* features of occurrences. Each single quantity feature is subsetting the root feature tensorQuantities.
* In other words, the codomain of a quantity feature is a suitable specialization of TensorQuantityValue.
*/
}
abstract attribute vectorQuantities: VectorQuantityValue[*] nonunique :> tensorQuantities;
abstract attribute scalarQuantities: ScalarQuantityValue[*] nonunique :> vectorQuantities;
abstract attribute def '3dVectorQuantityValue' :> VectorQuantityValue, ThreeVectorValue {
doc
/*
* Most general representation of real 3-vector quantities
*/
attribute :>> num: Real[3];
}
alias ThreeDVectorQuantityValue for '3dVectorQuantityValue';
/*
* Define generic aliases QuantityValue and quantities for the top level quantity attribute def and attribute.
*/
alias QuantityValue for TensorQuantityValue;
alias quantities for tensorQuantities;
attribute def SystemOfQuantities {
doc
/*
* A SystemOfQuantities represents the essentials of [VIM] concept "system of quantities" (https://jcgm.bipm.org/vim/en/1.3.html), defined as a
* "set of quantities together with a set of noncontradictory equations relating those quantities".
* In order to establish such a set of noncontradictory equations a set of base quantities is selected. Subsequently the system of quantities is
* completed by adding derived quantities which are products of powers of the base quantities.
*/
attribute baseQuantities: ScalarQuantityValue[*] ordered :> scalarQuantities;
}
attribute def QuantityPowerFactor {
doc
/*
* Representation of a quantity power factor, being the combination of a quantity and an exponent.
*
* A sequence of QuantityPowerFactors for the baseQuantities of a SystemOfQuantities define the QuantityDimension of a scalar quantity.
*/
attribute quantity: ScalarQuantityValue[1];
attribute exponent: Real[1];
}
attribute def QuantityDimension {
doc
/*
* Representation of quantity dimension, which is the product of powers of the set of base quantities defined for a particular system of quantities, units and scales.
*/
attribute quantityPowerFactors: QuantityPowerFactor[*] ordered;
}
}
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