--- title: "FormulaLookup" language: "en" type: "Symbol" summary: "FormulaLookup[query] gives a list of the full names of formulas whose names are consistent with query. FormulaLookup[query, n] returns at most n results. FormulaLookup[class] returns the names of all formulas within that class." keywords: - FormulaData - Formula - Lookup canonical_url: "https://reference.wolfram.com/language/ref/FormulaLookup.html" source: "Wolfram Language Documentation" related_guides: - title: "Formulas" link: "https://reference.wolfram.com/language/guide/Formulas.en.md" related_functions: - title: "FormulaData" link: "https://reference.wolfram.com/language/ref/FormulaData.en.md" - title: "MathematicalFunctionData" link: "https://reference.wolfram.com/language/ref/MathematicalFunctionData.en.md" --- # FormulaLookup FormulaLookup["query"] gives a list of the full names of formulas whose names are consistent with "query". FormulaLookup["query", n] returns at most n results. FormulaLookup["class"] returns the names of all formulas within that class. ## Details and Options * ``FormulaLookup[All]`` gives a full list of formula names. * ``FormulaLookup["Classes"]`` returns a full list of formula classes. * The following options can be given: | | | | | --------------------------- | -- | ------------------------------------ | | RequiredPhysicalQuantities | {} | which physical quantities to require | | ExcludedPhysicalQuantities | {} | which physical quantities to exclude | * Supported physical quantities include both physical and chemical quantities such as ``"Length"``, ``"ElectricCurrent"``, and ``"ChemicalPotential"``, as well as mathematical and financial quantities such as ``"Angle"`` and ``"Money"``. --- ## Examples (17) ### Basic Examples (2) Discover the full names of formulas for use in ``FormulaData`` : ```wl In[1]:= FormulaLookup["ohm's law"] Out[1]= {"OhmsLaw"} In[2]:= FormulaData["OhmsLaw"] Out[2]= V == I R ``` --- Find all formulas for a query: ```wl In[1]:= FormulaLookup["pendulum"] Out[1]= {{"PendulumSmallOscillations", "Standard"}, {"PendulumSmallOscillations", "Inertia"}, {"Pendulum", "Standard"}, {"Pendulum", "Inertia"}} ``` ### Scope (3) Limit the number of formulas displayed: ```wl In[1]:= FormulaLookup["moment of inertia formula", 4] Out[1]= {"ParallelAxisTheorem", "ConeMomentOfInertia", "CuboidMomentOfInertia", "CylinderMomentOfInertia"} ``` --- Find all available athletics formulas: ```wl In[1]:= FormulaLookup["Athletics"] Out[1]= {"BaseballBattingAverage", "BaseballGameScore", "BaseballIsolatedPower", "BaseballOnBasePercentagePlusSluggingPercentage", "BaseballPythagoreanWinExpectancy", "BaseballRangeFactor", "BaseballSluggingPercentage", {"BaseballBattingAverageOnBallsInPla ... "PullUpRepetitions", "PushUpRepetitions", "SitUpRepetitions", {"RowingMachine", "Speed"}, {"RowingMachine", "Pace"}, {"Running", "Speed"}, {"Running", "Pace"}, {"Swimming", "Speed"}, {"Swimming", "Pace"}, {"Walking", "Speed"}, {"Walking", "Pace"}} ``` --- Find all formula classes: ```wl In[1]:= FormulaLookup["Classes"] Out[1]= {"Athletics", "Chemistry", "EarthScience", "Engineering", "EverydayLife", "Finance", "Health&Medicine", "LifeSciences", "Mathematics", "Physics", "Space", "TechnologicalWorld", "Units", {"Athletics", "AmericanFootball"}, {"Athletics", "Baseball"}, ... "Space", "Astrodynamics"}, {"Space", "Astronomy"}, {"Space", "Astrophysics"}, {"Space", "Cosmology"}, {"TechnologicalWorld", "Advertising"}, {"TechnologicalWorld", "Automobiles"}, {"TechnologicalWorld", "Photography"}, {"Units", "UnitConversion"}} ``` ### Options (9) #### RequiredPhysicalQuantities (5) Limit the results by specifying a list of required physical quantities: ```wl In[1]:= FormulaLookup["moment of inertia formula", RequiredPhysicalQuantities -> {"Radius"}] Out[1]= {"ConeMomentOfInertia", "CylinderMomentOfInertia", "DiskMomentOfInertia", "SphereMomentOfInertia"} ``` --- Several necessary physical quantities can be specified: ```wl In[1]:= FormulaLookup["moment of inertia formula", RequiredPhysicalQuantities -> {"Radius", "Height"}] Out[1]= {"ConeMomentOfInertia", "CylinderMomentOfInertia"} ``` --- Include both required physical quantities and physical quantities to be excluded: ```wl In[1]:= FormulaLookup["moment of inertia formula", RequiredPhysicalQuantities -> {"Radius"}, ExcludedPhysicalQuantities -> {"Height"}] Out[1]= {"DiskMomentOfInertia", "SphereMomentOfInertia"} ``` --- Examine all formulas with specified physical quantities: ```wl In[1]:= FormulaLookup[All, RequiredPhysicalQuantities -> {"Distance", "Mass"}] Out[1]= {"MinimumPowerRequiredToMoveObject", "NewtonsLawOfUniversalGravitation", {"Work", "Acceleration"}, {"InclinedPlaneRolling", "PureRollingSpeedDistanceVelocity", "Slope", "MomentOfInertia"}, {"InclinedPlaneRolling", "PureRollingSpeedDistanceVelocity" ... a"}, {"InclinedPlaneRolling", "PureRollingSpeedDistanceVelocity", "Slope", "MomentOfInertia", "GravitationalAcceleration"}, {"InclinedPlaneRolling", "PureRollingSpeedDistanceVelocity", "SlopeAngle", "MomentOfInertia", "GravitationalAcceleration"}} ``` --- Find physics formulas using speed, distance and height: ```wl In[1]:= FormulaLookup["Physics", RequiredPhysicalQuantities -> {"Speed", "Distance", "Height"}] Out[1]= {"Projectile", "ThrowingAngle"} ``` #### ExcludedPhysicalQuantities (4) Limit the results by specifying a list of excluded physical quantities: ```wl In[1]:= FormulaLookup["moment of inertia formula", ExcludedPhysicalQuantities -> {"Height"}] Out[1]= {"CuboidMomentOfInertia", "DiskMomentOfInertia", "EllipticalLaminaMomentOfInertia", "ParallelAxisTheorem", "PointMassMomentOfInertia", "SolidEllipsoidMomentOfInertia", "SphereMomentOfInertia", "ThinRodMomentOfInertia", "TriangularPlateMomentOfInertia"} ``` --- Several necessary physical quantities can be specified: ```wl In[1]:= FormulaLookup["moment of inertia formula", ExcludedPhysicalQuantities -> {"Radius", "Height"}] Out[1]= {"CuboidMomentOfInertia", "EllipticalLaminaMomentOfInertia", "ParallelAxisTheorem", "PointMassMomentOfInertia", "SolidEllipsoidMomentOfInertia", "ThinRodMomentOfInertia", "TriangularPlateMomentOfInertia"} ``` --- Include both required physical quantities and physical quantities to be excluded: ```wl In[1]:= FormulaLookup["moment of inertia formula", RequiredPhysicalQuantities -> {"Radius"}, ExcludedPhysicalQuantities -> {"Height"}] Out[1]= {"DiskMomentOfInertia", "SphereMomentOfInertia"} ``` --- Find all formulas with specified physical quantities but not including other physical quantities: ```wl In[1]:= FormulaLookup[All, 10, RequiredPhysicalQuantities -> {"Distance", "Mass"}, ExcludedPhysicalQuantities -> {"SlopeAngle", "Work", "Length"}] Out[1]= {"MinimumPowerRequiredToMoveObject", "NewtonsLawOfUniversalGravitation", {"InclinedPlaneRolling", "PureRollingSpeedDistanceVelocity", "Slope", "MomentOfInertia"}, {"InclinedPlaneRolling", "PureRollingSpeedDistanceVelocity", "SlopeAngle", "MomentOfInertia"}, {"InclinedPlaneRolling", "PureRollingSpeedDistanceVelocity", "Slope", "MomentOfInertia", "GravitationalAcceleration"}, {"InclinedPlaneRolling", "PureRollingSpeedDistanceVelocity", "SlopeAngle", "MomentOfInertia", "GravitationalAcceleration"}} ``` ### Applications (1) Find all formulas for the moment of inertia: ```wl In[1]:= formulas = FormulaLookup["moment of inertia", 20] Out[1]= {"ParallelAxisTheorem", "ConeMomentOfInertia", "CuboidMomentOfInertia", "CylinderMomentOfInertia", "DiskMomentOfInertia", "EllipticalLaminaMomentOfInertia", "PointMassMomentOfInertia", "SolidEllipsoidMomentOfInertia", "SphereMomentOfInertia", "ThinRodMomentOfInertia", "TriangularPlateMomentOfInertia"} In[2]:= Grid[{#, FormulaData[#]}& /@ formulas, Frame -> All] Out[2]= | | | | --------------------------------- | ------------------------------------------------ | | "ParallelAxisTheorem" | I∥ == m r^2 + ICM ... a" | I == (2/5) m r^2 | | "ThinRodMomentOfInertia" | {I∥ == 0, I⊥ == (1/12) l^2 m} | | "TriangularPlateMomentOfInertia" | Iz == (1/36) (a^2 + b^2 + c^2) m | ``` ### Possible Issues (1) Many formulas have multiple forms: ```wl In[1]:= FormulaLookup["planck's law"] Out[1]= {{"PlanckRadiationLaw", "Wavelength"}, {"PlanckRadiationLaw", "Frequency"}} In[2]:= Column[{FormulaData[{"PlanckRadiationLaw", "Wavelength"}], FormulaData[{"PlanckRadiationLaw", "Frequency"}]}] Out[2]= L[λ] == (Quantity[2, "PlanckConstant"*"SpeedOfLight"^2]/(-1 + E^(Quantity[1, ("PlanckConstant"*"SpeedOfLight")/"BoltzmannConstant"]/T λ)) λ^5) L[ν] == ((Quantity[2, "PlanckConstant"/"SpeedOfLight"^2]) ν^3/-1 + E^((Quantity[1, "PlanckConstant"/"BoltzmannConstant"]) ν/T)) ``` ### Interactive Examples (1) Dynamically examine formulas with specific physical quantities: ```wl In[1]:= pqs = {"Time", "Length", "Mass", "Frequency", "Speed", "Energy", "Power"}; Manipulate[ formulas = FormulaLookup[All, 1000, RequiredPhysicalQuantities -> {pq1, pq2, pq3}]; If[formulas === {}, Style["no formulas found", Gray], Pane[Column[ Column[{Style[#, Bold], Column[Flatten[{FormulaData[#, "Formula"]}]], FormulaData[#, "QuantityVariableTable"]}] & /@ formulas, Dividers -> Center], {Automatic, 500}, Scrollbars -> True]], {{pq1, "Time", "phys. quant. 1"}, pqs, SetterBar}, {{pq2, "Length", "phys. quant. 2"}, pqs, SetterBar}, {{pq3, "Speed", "phys. quant. 3"}, pqs, SetterBar}, SaveDefinitions -> True] Out[1]= DynamicModule[«8»] ``` ## See Also * [`FormulaData`](https://reference.wolfram.com/language/ref/FormulaData.en.md) * [`MathematicalFunctionData`](https://reference.wolfram.com/language/ref/MathematicalFunctionData.en.md) ## Related Guides * [`Formulas`](https://reference.wolfram.com/language/guide/Formulas.en.md) ## History * [Introduced in 2014 (10.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn100.en.md)