Exploring Analyic Geometry with Mathematica®

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Error Messages

Arc2D
Circle2D
ConicArc2D
D2DExpressions2D
D2DMaster$2D
Directrices2D
Ellipse2D
Hyperbola2D
IsNumeric2D
Line2D
Loci2D
MedialEquations2D
Parabola2D
Parameters2D
Point2D
Quadratic2D
Segment2D
Sketch2D
Solve2D
SolveTriangle2D
TangentConics2D
Transform2D
Triangle2D

This chapter is a listing of all the error messages that can be generated by Descarta2D during computations. Mathematica may generate additional error messages. The messages are listed alphabetically by message name. The number in square brackets indicates the page where the error is defined in the packages.

Arc2D [Top]

Arc2D::collinear

No arc exists; the given points {"errors_1.gif","errors_2.gif","errors_3.gif"} are collinear.

When specifying an arc through three points, the points cannot be collinear. Descarta2D will return the $Failed symbol if it detects that the three specified points lie on a line.

Arc2D::imaginary

An invalid arc of the form arc"errors_4.gif" has been detected; the arguments cannot be imaginary.

The arguments of an arc cannot involve imaginary numbers. Descarta2D will return the $Failed symbol whenever the arguments of an object are determined to be invalid.

Arc2D::invalid

An invalid arc of the form arc has been detected; the bulge factor must be positive and the defining points must be distinct.

The bounding points of an arc cannot be coincident and the bulge factor must be positive. Descarta2D will return the $Failed symbol whenever the arguments of an object are determined to be invalid.

Arc2D::invalidCoincident

The defining points are coincident; an arc cannot be constructed.

The defining points of an arc must be distinct. Descarta2D will return the $Failed symbol if coincident points are detected.

Arc2D::invalidCollinear

The three defining points are collinear; an arc cannot be constructed.

An arc cannot be constructed through three collinear points. Descarta2D will return the $Failed symbol if collinear points are detected.

Arc2D::invalidEntryAngle

The entry angle of the arc is invalid; the entry angle cannot be an integer multiple of Pi radians.

The entry angle of an arc cannot be an integer multiple of π radians. Descarta2D will return the $Failed symbol if invalid entry angle is detected.

Arc2D::invalidRadius

The radius, r, of the arc is invalid; the radius must be positive.

The radius of an arc must be positive. Descarta2D will return the $Failed symbol if a non-positive radius is detected.

Arc2D::invalidSpan

The angular span of the arc is invalid; the span cannot be an integer multiple of 2Pi radians.

The angular span of an arc cannot be a multiple of radians. The $Failed symbol will be returned when an invalid span is specified.

Circle2D [Top]

Circle2D::coincident

The points {"errors_5.gif","errors_6.gif"} are coincident; no valid circle exists.

When specifying a circle by two points, the points cannot be coincident. Descarta2D will return the $Failed symbol if two coincident points are specified.

Circle2D::collinear

The points {"errors_7.gif","errors_8.gif","errors_9.gif"} are collinear; no valid circle exists.

When specifying a circle through three points, the points cannot be collinear. Descarta2D will return the $Failed symbol if it detects that the three specified points lie on a line.

Circle2D::imaginary

An invalid circle of the form cir"errors_10.gif" has been detected; the arguments cannot be imaginary.

The arguments defining a circle cannot be imaginary numbers. Descarta2D will return the $Failed symbol if the arguments of an object involve imaginary numbers.

Circle2D::invalid

An invalid circle of the form cir"errors_11.gif" has been detected; the radius must be positive.

When defining a circle the radius must be a positive number. Descarta2D will return the $Failed symbol whenever the arguments to an object are determined to be invalid.

Circle2D::noCircle

The curve represented by "errors_12.gif" is not a circle.

Descarta2D has detected that the curve represented by a Quadratic2D is not a circle. The $Failed symbol will be returned.

Circle2D::on

"errors_13.gif" is on "errors_14.gif"; no valid circle exists.

When specifying a circle tangent to a line with a given center point, the point cannot be on the line. If Descarta2D detects that the point lies on the line, it will return the $Failed symbol.

Circle2D::radius

The radius argument, r, is invalid; the radius must be positive.

When specifying a circle by center point and radius, the radius must be positive. Descarta2D will return the $Failed symbol if a non-positive radius is specified during a circle construction.

ConicArc2D [Top]

ConicArc2D::center

The chord defined by ln"errors_15.gif" passes through the center of crv"errors_16.gif"; a conic arc cannot be constructed.

The chord of a conic arc cannot pass through the center of a central conic because this configuration is invalid. If the line defining the chord passes through the center of the conic, then the $Failed symbol will be returned.

ConicArc2D::imaginary

An invalid conic arc of the form cnarc"errors_17.gif" has been detected; the arguments cannot be imaginary.

The arguments defining a conic arc cannot be imaginary. If Descarta2D detects an invalid object the $Failed symbol will be returned.

ConicArc2D::noChord

No chord exists between ln"errors_18.gif" and crv"errors_19.gif"; a conic arc cannot be constructed.

When constructing a conic arc from a line and a conic curve, the line must intersect the conic in two points that form the chord of the conic arc. If the intersection consists of less than two points, or it is on opposite branches of a hyperbola, then the $Failed symbol will be returned.

ConicArc2D::points

An invalid conic arc of the form cnarc"errors_20.gif" has been detected; the control points cannot be collinear.

The three control points defining a conic arc cannot be collinear. Descarta2D will return the $Failed symbol whenever the arguments to an object are determined to be invalid.

ConicArc2D::rho

An invalid conic arc of the form cnarc"errors_21.gif" has been detected; the value of rho must be in the range 0<rho<1.

The value of ρ determines the shape and type of the conic arc. When 0<ρ<1/2 an elliptic conic arc is created, when ρ=1/2 a parabolic conic arc is created and when 1/2<ρ<1 a hyperbolic conic arc is created. Descarta2D will return the $Failed symbol whenever the arguments to an object are determined to be invalid.

D2DExpressions2D [Top]

D2DExpressions2D:badTol

The tolerance tol is not a valid tolerance specification; the default tolerance, "errors_22.gif", will be used.

Tolerance values used to query expressions must be numbers greater than or equal to zero.

D2DMaster$2D [Top]

D2DMaster$2D::loaded

The package `D2DMaster2D' has already been loaded.

The package D2DMaster2D.m defines the symbol names associated with each Descarta2D package so that it can be loaded automatically when referenced. This file only needs to be loaded once; subsequent requests to load the file will be ignored and will cause no harm.

D2DMaster$2D::noPath

The path to 'D2DMaster2D.m' cannot be found; unable to initialize Descarta2D.

The package D2DMaster2D.m defines the symbol names associated with each Descarta2D package so that it can be loaded automatically when referenced. This error indicates that the software has not been installed correctly.

D2DMaster$2D::tooManyPaths

More than one path to 'D2DMaster2D.m' was found; using path-name.

The package D2DMaster2D.m defines the symbol names associated with each Descarta2D package so that they can be loaded automatically when referenced. This error indicates that the software has found more than one copy of this file and may suggest that the software has not been installed correctly.

Directrices2D [Top]

Directrices2D::circular

The ellipse "errors_23.gif" is circular; it has no (finite) directrix lines.

An ellipse whose semi-major and semi-minor axes are equal in length has no (finite) directrix lines. Descarta2D will return an empty list.

Ellipse2D [Top]

Ellipse2D::imaginary

An invalid ellipse of the form ellipse"errors_24.gif" has been detected; the arguments of an ellipse cannot involve imaginary numbers.

When constructing an ellipse Descarta2D verifies that none of the arguments involve imaginary numbers. Descarta2D will return the $Failed symbol whenever the arguments to an object are determined to be invalid.

Ellipse2D::invalid

An invalid ellipse of the form ellipse"errors_25.gif" has been detected; the length of both the semi-major and semi-minor axes must be positive.

When constructing an ellipse Descarta2D verifies that both the semi-major and semi-minor axes have positive lengths. Descarta2D will return the $Failed symbol whenever the arguments to an object are determined to be invalid.

Ellipse2D::invdef

The defining geometry or eccentricity is invalid; the eccentricity of an ellipse must be in the range 0<e<1, the foci and vertices cannot be coincident, and the focus cannot lie on the directrix.

An invalid ellipse was specified and Descarta2D will return the $Failed symbol.

Hyperbola2D [Top]

Hyperbola2D::imaginary

An invalid hyperbola of the form hyp"errors_26.gif" has been detected; the arguments cannot be imaginary.

When constructing a hyperbola the arguments cannot be imaginary. If imaginary arguments are detected Descarta2D will return the $Failed symbol.

Hyperbola2D::invalid

An invalid hyperbola of the form hyp"errors_27.gif" has been detected; the lengths of the semi-transverse and semi-conjugate axes must be positive.

When constructing a hyperbola the lengths of both the semi-transverse and the semi-conjugate axes must be positive. Descarta2D will return the $Failed symbol whenever the arguments to an object are determined to be invalid.

Hyperbola2D::invdef

The defining geometry or eccentricity is invalid; the eccentricity of a hyperbola must be greater than 1, the foci and vertices cannot be coincident and the focus cannot lie on the directrix.

An invalid hyperbola was specified and Descarta2D will return the $Failed symbol.

IsNumeric2D [Top]

IsNumeric2D:notNumeric

The funcName function requires numerical arguments; symbolic arguments are not allowed.

Some Descarta2D functions require that their arguments be numeric. These functions will not allow symbolic arguments.

Line2D [Top]

Line2D::concentric

The circles {"errors_28.gif","errors_29.gif"} are concentric; no radical axis exists.

When specifying the two circles for the construction of a radical axis, the two circles cannot be concentric. If Descarta2D detects that concentric circles have been specified in the radical axis construction, it will return the $Failed symbol.

Line2D::imaginary

An invalid line of the form ln"errors_30.gif" has been detected; the arguments cannot be imaginary.

The arguments defining a line cannot be imaginary. If Descarta2D detects that an object is invalid the $Failed symbol will be returned.

Line2D::invalid

An invalid line of the form ln"errors_31.gif" has been detected; at least one of the first two coefficients must be non-zero.

When defining a line at least one of the first two coefficients, A or B, must be non-zero. Descarta2D will return the $Failed symbol whenever the arguments to an object are determined to be invalid.

Line2D::noPolar

Since pt"errors_32.gif" is at the center of the conic, no polar line exists.

When creating the polar line of a quadratic with respect to a point, Descarta2D verifies that the point is not coincident with the center of the conic curve represented by the quadratic. If the point is at the center of the conic represented by the quadratic Descarta2D returns the $Failed symbol.

Line2D::noPoly

The expression expr cannot be recognized as a linear polynomial or equation in variables x and y.

When converting a polynomial or equation to a line, the expression representing the line must be recognizable as a linear polynomial or equation. If the expression is not recognizable Descarta2D returns the $Failed symbol.

Line2D::sameCoords

The coordinates {"errors_33.gif","errors_34.gif"} and {"errors_35.gif","errors_36.gif"} are coincident; no valid line can be constructed.

When creating a line through a pair of coordinates or a pair of points, the positions cannot be coincident. Descarta2D will return the $Failed symbol if it detects the coordinates are coincident.

Loci2D [Top]

Loci2D::central

The quadratic is a central conic, but its type cannot be determined.

Due to the nature of the coefficients of the quadratic, the specific conic type cannot be determined; an empty list will be returned.

Loci2D::eccentricity

The eccentricity, e, is invalid; the eccentricity must be positive.

The eccentricity of a conic must be positive; the $Failed symbol will be returned.

Loci2D::noLocus

The quadratic has no real locus.

The equation represented by the quadratic has no real points; an empty list will be returned.

MedialEquations2D [Top]

MedialEquations2D::coincident

The objects {"errors_37.gif","errors_38.gif"} are coincident; no finite number of medial curves exist.

When two objects are identical the medial points include all the points in the plane and no unique curve locus exists. When this situation occurs Descarta2D will return an empty list indicating that no unique curves satisfy the geometric constraints specified.

Parabola2D [Top]

Parabola2D::imaginary

An invalid parabola of the form parabola"errors_39.gif" has been detected; the arguments cannot be imaginary.

The arguments of a parabola cannot be imaginary. Descarta2D will return the $Failed symbol whenever the arguments to an object are determined to be invalid.

Parabola2D::invalid

An invalid parabola of the form parabola"errors_40.gif" has been detected; the focal length cannot be zero.

The focal length, f, of a parabola cannot be zero. Descarta2D will return the $Failed symbol whenever the arguments to an object are determined to be invalid.

Parabola2D::invptln

The focus pt"errors_41.gif" is on the directrix ln"errors_42.gif"; no valid parabola can be constructed.

The focus point of a parabola cannot be on the directrix line. Descarta2D returns the $Failed symbol when it detects an invalid construction.

Parameters2D [Top]

Parameters2D::noChord

No chord exists between "errors_43.gif" and "errors_44.gif".

The Parameters2D function requires that the defining line intersect the curve in two points. If the line does not intersect the chord, Descarta2D will return the $Failed symbol.

Point2D [Top]

Point2D::coincident

No unique intersection point exists; lines ln"errors_45.gif" and ln"errors_46.gif" are coincident.

Coincident lines cannot be intersected. Descarta2D will return the $Failed symbol if it detects an attempt to intersect coincident lines.

Point2D::imaginary

An invalid point of the form pt"errors_47.gif" has been detected; the coordinates of a point cannot be imaginary.

The coordinates of a point cannot be imaginary. If Descarta2D detects an invalid object the $Failed symbol will be returned.

Point2D::noDir

Points {"errors_48.gif","errors_49.gif"} are coincident and do not define a valid direction.

When defining a point that is offset in a direction specified by two points, the direction points cannot be coincident. Descarta2D returns the $Failed symbol if the two points are coincident.

Point2D::noPole

Since ln"errors_50.gif" passes through the center of the conic, no pole point exists.

When creating the pole point of a quadratic with respect to a line, Descarta2D verifies that the line does not pass through the center of the conic curve represented by the quadratic. If the line does pass through the center Descarta2D returns the $Failed symbol.

Point2D::noRatio

The sum of the ratio numbers {"errors_51.gif","errors_52.gif"} cannot be zero.

When defining a point that divides a segment into a given ratio, the ratio numbers "errors_53.gif" and "errors_54.gif" cannot sum to zero. Descarta2D will return the $Failed symbol if the ratio numbers are invalid.

Point2D::notCentral

quad is not a central conic; it has no center point.

The quadratic is not a central conic and has no center point. Descarta2D will return the $Failed symbol.

Point2D::notCentral1

The conic underlying cnarc is not a central conic; it has no center point.

The conic underlying a conic arc is not a central conic and has no center point. Descarta2D will return the $Failed symbol.

Point2D::parallel

No intersection point exists; lines ln"errors_55.gif" and ln"errors_56.gif" are parallel.

Parallel lines cannot be intersected. Descarta2D will return the $Failed symbol if its detects an attempt to intersect parallel lines.

Quadratic2D [Top]

Quadratic2D::coincident

Two or more of the points are coincident; no valid quadratic pencil exists.

When constructing a quadratic pencil from four points, no pair of points may be coincident. The $Failed symbol with be returned if any pair of points is detected to be coincident.

Quadratic2D::eccentricity

The eccentricity e is invalid; the eccentricity must be positive.

When defining a quadratic using a point, a line and an eccentricity, Descarta2D will report an error if the eccentricity is not positive and return the $Failed symbol.

Quadratic2D::imaginary

An invalid quadratic of the form quad"errors_57.gif" has been detected; the arguments cannot be imaginary.

The arguments defining a quadratic cannot be imaginary. If Descarta2D detects that an object is invalid the $Failed symbol will be returned.

Quadratic2D::invalid

An invalid quadratic of the form quad"errors_58.gif" has been detected; at least one of the first five coefficients must be non-zero.

At least one of the first five coefficients of a quadratic must be non-zero. The $Failed symbol is returned whenever the arguments to an object are determined to be invalid.

Quadratic2D::invEcc

A negative eccentricity, expr"errors_59.gif", is invalid; no valid quadratic can be constructed.

The eccentricity of a conic must be non-negative. Descarta2D will return the $Failed symbol if an invalid eccentricity is specified.

Quadratic2D::invLen

A non-positive focal chord length, expr"errors_60.gif", is invalid; no valid quadratic can be constructed.

The length of a conic's focal chord must be positive. Descarta2D will return the $Failed symbol if an invalid length is specified.

Quadratic2D::noPoly

The expression expr cannot be recognized as a quadratic polynomial or equation in variables x and y.

When converting a polynomial or equation to a quadratic, the expression representing the quadratic must be recognizable as a quadratic polynomial or equation. If the expression is not recognizable Descarta2D returns the $Failed symbol.

Segment2D [Top]

Segment2D::imaginary

An invalid line segment of the form lnseg"errors_61.gif" has been detected; the arguments cannot be imaginary.

A line segment with imaginary arguments has been detected. Descarta2D will return the $Failed symbol whenever the arguments to an object are determined to be invalid.

Segment2D::invalid

An invalid line segment of the form lnseg"errors_62.gif" has been detected; the defining coordinates cannot be coincident.

In order to be valid, a line segment must have two distinct end points, they cannot be coincident. Descarta2D will return the $Failed symbol whenever the arguments to an object are determined to be invalid.

Sketch2D [Top]

Sketch2D::invalidLength

Setting CurveLength2D"errors_63.gif" is invalid; `CurveLength2D' must be positive; the current value of CurveLength2D"errors_64.gif" will be retained.

When using the Mathematica SetOptions command, any attempt to set the CurveLength2D parameter of the Sketch2D function to a non-positive value will be rejected. The current value of the CurveLength2D parameter will be retained.

Sketch2D::noObj

No valid objects to sketch.

If there are no valid geometric objects in the list of objects to sketch, Descarta2D will output the Sketch2D::noObj message to indicate no graphical output will be plotted.

Sketch2D::notReal

n object(s) cannot be sketched.

When plotting objects using the Sketch2D command, Descarta2D will count the number of objects that have symbolic arguments. Such objects cannot be plotted and will not be included in the graphics that are displayed.

Solve2D [Top]

Solve2D::infinite

An infinite number of solutions exist; only independent solutions will be returned.

When solving a system of equations some solutions may exist in which the solutions are interrelated functions of each other. Such solutions will not be returned.

Solve2D::invalidTime

Option MaxSeconds2D->"errors_65.gif" is invalid; 'MaxSeconds2D' must be positive; the current value of MaxSeconds2D->"errors_66.gif" will be retained.

When setting the MaxSeconds2D option of the Solve2D command, the option value must be positive.

Solve2D::time

The equations could not be solved in MaxSeconds2D->n"errors_67.gif", an empty list of solutions will be returned; using approximate numbers may produce a more complete list of solutions.

Some equations are too complex to be solved in the time allowed by the Descarta2D Solve2D command. An empty list of solutions will be returned if the maximum time elapses before a solution is found. To increase the maximum time allowed use the SetOptions command. For example,

SetOptions[Solve2D,MaxSeconds2D->60].

will set the time limit to 60 seconds.

SolveTriangle2D [Top]

SolveTriangle2D::ambiguous

Two valid solutions exist for this configuration; set the alternate solution option to logical to compute the other configuration.

When computing a triangle configuration, Descarta2D will display this warning if more than one solution is valid. The logical will either be True or False indicating the setting required to produce the alternate configuration.

SolveTriangle2D::anglesOnly

The triangle configuration is under-constrained; a valid configuration with the triangle's perimeter arbitrarily set to 1 will be computed.

When computing a triangle configuration consisting of angles only, Descarta2D will display this warning to indicate that the length of the sides are arbitrarily set, being correct for the given angles.

SolveTriangle2D::constrain

The triangle configuration is under-constrained; three constraints are expected.

At least three parameters are needed to compute a triangle configuration. Descarta2D will return $Failed if a configuration is under-constrained.

SolveTriangle2D::invConfig

The configuration of sides and/or angles specified is invalid; no triangle can be constructed.

An invalid triangle configuration has been specified. Descarta2D will return $Failed.

TangentConics2D [Top]

TangentConics2D::coincident

Two or more of the defining points or lines are coincident; no proper conic can be constructed.

When constructing a tangent conic from defining points, all of the points must be unique; if any of the points are coincident, Descarta2D will return an empty list.

TangentConics2D::collinear

Three or more of the defining points are collinear; no proper conic can be constructed.

When constructing a tangent conic from defining points, no triple of three points may be collinear; if any triple is collinear Descarta2D will return an empty list.

TangentConics2D::concurrent

Three or more of the tangent lines are concurrent; no proper conic can be constructed.

When constructing a tangent conic from defining lines, no triple of lines can be concurrent (meet in a point); if any triple is concurrent Descarta2D will return an empty list.

TangentConics2D::linesThru

One of the points is on more than one of the tangent lines; no proper conic can be constructed.

When constructing a tangent conic from points and lines, each point is allowed to be on at most one of the tangent lines; if any point is on more than one line, Descarta2D will return an empty list.

TangentConics2D::parallel

Three or more of the defining lines are parallel; no proper conic can be constructed.

When constructing a tangent conic from defining lines, no triple of lines can be parallel; if any triple is parallel Descarta2D will return an empty list.

TangentConics2D::pointsOn

Two or more of the points are on a tangent line; no proper conic can be constructed.

When constructing a tangent conic from points and lines, each line can have at most one point on it; if any line has more than one point one it, Descarta2D will return an empty list.

Transform2D [Top]

Transform2D::invalidScale

The scale factor s is invalid; the scale factor must be positive.

The scale factor, s, for a scaling transformation must be positive. Descarta2D will return the $Failed symbol if a non-positive scale factor is specified.

Triangle2D [Top]

Triangle2D::imaginary

An invalid triangle of the form triangle"errors_68.gif" has been detected; the arguments cannot be imaginary.

The arguments of a triangle cannot be imaginary. Descarta2D will return the $Failed symbol whenever the arguments to an object are determined to be invalid.

Triangle2D::invalid

An invalid triangle of the form triangle"errors_69.gif" has been detected; the vertex points cannot be collinear.

The vertex points of a triangle cannot be collinear. Descarta2D will return the $Failed symbol whenever the arguments to an object are determined to be invalid.

Triangle2D::noTriangle

Two of the lines {"errors_70.gif","errors_71.gif","errors_72.gif"} are parallel, or the three are concurrent; no triangle exists.

When defining a triangle by three lines, the lines must intersect in three distinct points. If any pair of lines are parallel, or the three lines are concurrent, Descarta2D will return the $Failed symbol.


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