Quick-Reference Tips
These quick-reference tips assume the reader is somewhat familiar
with Converse mode's full documentation,
but wants a concise summary of the tips and tricks scattered
throughout. The tips are grouped by subject and follow the
same outline as the Detailed
Coverage section:
Major Styles of Input
(more...)
- Spaces around mathematical symbols (+-*/:()=%), commas, and semi-colons are
optional, but required between "x" and a non-numeric operand. (e.g. "1+1", "2 + 3", "2x4", "length x width")
- Most punctuation symbols (.,;?!) can be used normally.
Major
Categories of Input (more...)
- AutoMathic does NOT handle "yes or no" questions. (e.g. "Is the mass 5 unit kg?")
- Any inconsistency must be resolved following such a warning
message.
- Kernel commands may not be mixed with other input, and must
begin with the "Kernel escape" character. It is "!" by
default, but may be redefined in the "config" setup file or
using a kernel command (e.g. "!set c_kernel_esc=#")
- By default, AutoMathic will utilize its library without asking unless the "b_auto_consult" option
is set to "0".
Literal Numbers (more...)
- Numbers may contain commas (,) as group separators. (e.g. 1,000,000)
- Decimal fractions between -1 and 1 MUST have a leading zero.
(e.g. -0.125)
- Numbers may NOT be entered using scientific notation. (e.g. 3.215e-9)
Written
Numbers (more...)
- Written numbers can always be combined as long as the
combination is multiplicative, not additive. (e.g. "three hundred", "five sixteenths", "5
16ths")
- Numeric "fraction words" (e.g. "3rds", "10ths",
"16ths", etc.) are understood and translated as
expected, whether or not they appear after a "/", supporting
natural-looking input styles for fractions. (e.g. , "2 3rds",
"2/3rds", "5 16ths", "5/16ths")
- Contrary to standard spelling conventions, AutoMathic's
combined numbers must NOT be hyphenated. (e.g. "two-thirds")
- Additive combinations of numbers are safe when they are not
part of a larger term. (e.g. "three and a half")
- Complicated written numbers (that imply multiplication and
addition) are usually NOT understood by AutoMathic. (e.g. "two hundred fifty six")
- The only way to use an additive combination as part of a
larger term is to enclose the combination within parentheses to
help guide the translation. (e.g. "(three and a half) thousand")
- It is most effective to use written numbers for the simple
cases and multiplicative combinations only.
The Notion of Units (more...)
- If every measurement of the same type (e.g. length) uses the
same units, the units can be left off entirely.
- Units must be used when two or more measurements of the same
type (e.g. distance) use different units of measurement.
- If units are used for a type of measurement, include units for
every measurement of that type.
Units with Scalars
(more...)
- Unit abbreviations must
NOT include periods (e.g. "ft.") unless of course it appears at
the end of a sentence.
- Built-in abbreviations of compound units (e.g. MPH, FPS, RPM)
can be treated as simple units and not be parenthesized.
- In Unit Phrases,
simple or compound units can be enclosed in square brackets to
simplify and shorten the unit phrase.
- Put "measured in",
"in unit", or one
of their variants, between a property and its unit. (e.g. "length measured in inches",
"length in [inches]")
- Put "unit" or "units" between a
quantity and its unit (e.g. "15 unit cm"), unless the unit is enclosed
in square brackets. (e.g. "15[cm]")
- A compound unit following a quantity must be enclosed in
parentheses or square brackets. (e.g. "15 unit (miles per hour)", "15[miles per hour]")
- Parentheses are optional for a compound unit following a
property. (e.g. "speed in
unit miles per hour", or "speed in unit (miles per hour)")
- Parentheses are not required when a compound unit is enclosed
in square brackets. (e.g. "speed
in
[miles per hour]")
- Units can be used
by themselves (without scalars or properties) in a standalone
fashion. (e.g. "miles per
hour is 55")
- Unit phrases can be used by themselves to request a
calculation. (e.g. "speed
in units mph", "speed
in [mph]")
- Unit phrases can be used in questions to ask for a
measurement. (e.g. "How
many unit MPH would the speed be?", "How many [MPH] would the speed
be?")
- Unit phrases can be used in statements of fact to define a
measurement. (e.g "The
speed is 55 unit (mi/hr).", "The speed is 55[mph].")
Unit Conversion (more...)
e.g. Convert 55 unit mph into unit kph.
e.g. Convert 55[mph] into [kph].
e.g. 55 unit mph to units kph.
e.g. 55[mph] to [kph].
e.g. Convert 55 from unit mph to unit kph.
e.g. Convert 55 from [mph] to [kph].
e.g. 55 from units mph into units kph.
e.g. 55 from [mph] into [kph].
e.g. 55 converted from unit mph to unit kph.
e.g. 55 converted from [mph] to [kph].
e.g. How many unit kph converts to 55 unit mph?
e.g. How many [kph] converts to 55[mph]?
e.g. How many unit kph would 55 unit mph convert to?
e.g. How many [kph] would 55[mph] convert to?
- The following formal grammar describes AutoMathic's language
for units:
unit:
<simple unit>
<compound unit>
unit-phrase:
<property> {MEASURED IN|IN TERMS OF} [UNIT[S]] <unit>
<property> {MEASURED IN|IN TERMS OF} "["<unit>"]"
<property> IN UNIT[S] <unit>
<property> IN "["<unit>"]"
<quantity> UNIT[S] <simple unit>
<quantity> UNIT[S] (<compound unit>)
<quantity> "["<unit>"]"
<unit>
<unit-phrase>
[CONVERT] <unit-phrase> {IN|TO|INTO} UNIT[S] <unit>
[CONVERT] <unit-phrase> {IN|TO|INTO} "["<unit>"]"
[CONVERT] <quantity> FROM UNIT[S] <unit> {IN|TO|INTO} UNIT[S] <unit>
[CONVERT] <quantity> FROM "["<unit>"]" {IN|TO|INTO} "["<unit>"]"
<quantity> CONVERT[S|ED] FROM UNIT[S] <unit> {IN|TO|INTO} UNIT[S] <unit>
<quantity> CONVERT[S|ED] FROM "["<unit>"]" {IN|TO|INTO} "["<unit>"]"
<unit-phrase> CONVERT[S|ED] {IN|TO|INTO} <unit-phrase>
<unit-phrase> <helping-verb> <unit-phrase> CONVERT[S|ED] {IN|TO|INTO}
Temperature
Conversion (more...)
- Unit conversions for units that are not simple ratios of each
other (e.g. temperature scales) must be done using
property-based unit phrases. (e.g. "temperature measured in Celsius", or "temperature in units
Fahrenheit")
Mathematical Operators (more...)
- "+" - plus, added to, more than, larger than, greater than,
bigger than, higher than, later than, longer than, wider than,
taller than, deeper than, broader than, hotter than, heavier
than, faster than, quicker than, older than
and, &, less, smaller, fewer,
or, after, above, beyond, past, with
- "-" - minus, takeaway, take away, from, off, under, before,
below, sans, short of, subtracted from, taken from, taken away
from, less than, smaller than, fewer than, shy of, sooner than,
shorter than, narrower than, shallower than, colder than,
lighter than, lower than, slower than, younger than
more, larger, greater, bigger,
higher, without
- "*" - times, by, x, multiplied by
- "/" - over, to, :, divided by, divided in, divided into, out
of
<BE> to, <BE> {in|on}
<ARTICLE>, unit
- AutoMathic does not support exponents, roots, or high-level
math functions.
Variables (more...)
- AutoMathic creates variables out of nouns and noun phrases.
Nouns and Noun Phrases (more...)
- Noun phrases that include restrictive clauses get simplified.
(e.g. "cars that are red"
simplifies to "red")
- AutoMathic cannot handle problems requiring more than 52
variables.
Fuzzy-Matching (more...)
- AutoMathic can be explicitly told that unmatched references to
the same thing are the same via a statement of fact. (e.g. "goose means geese")
Quantity Words (more...)
- Quantity words that are part of a larger noun phrase have a
different interpretation than quantity words used by themselves.
(e.g. "percentage", "number", "amount", "fraction", "quantity",
"part", "portion", "multiple")
- Quantity words and mathematical constants (e.g. Pi, Tau, e,
Golden Ratio, C), are the only classes of nouns that have
special meaning to AutoMathic.
Implicit Nouns (more...)
- AutoMathic automatically solves for nouns that start with
"what" or "how much". (e.g. "Half of the total is what value?")
- AutoMathic automatically solves for implicit nouns that arise
from generic "how much", "how many", and "what" questions. (e.g.
"Six times how many is a
dozen?")
Mathematical Expressions (more...)
- A mathematical expression is some arithmetic combination of
numbers, operators, and variables.
Requests for calculation
and simple questions
translate into mathematical expressions.
- If AutoMathic says that it "didn't understand" something,
always rephrase the input to let it try again.
- Questions usually use a form of the verb "to be".
- AutoMathic does NOT handle "yes or no" questions! (e.g. "Is the mass 5 unit kg?")
Mathematical Equations (more...)
- A mathematical equation is simply two mathematical expressions
joined by an equals sign (=).
- Any assertion or statement of fact translates into an
equation.
- In Algebraic
style, equations are literally created by joining two
mathematical expressions with an equals sign.
- In Simple
Translation, equations are usually created using
variations of simple synonyms or idioms for the equals sign
(e.g. "equals", "is", "are", "was", "were", "make", "makes up",
"gives", "yields", "results in").
- In Natural Language,
equations can come from sentences with almost any verb phrase
based on the verb "to be".
- In Natural Language, non-trivial questions
can produce equations (which themselves are
"statements-of-fact").
- Statements of fact create equations and/or assign values to
variables.
- Equations with no
variables are ignored.
- Statements of fact
involving one "thing" assign a value to its variable.
- Statements of
fact involving two or more "things" form an equation
relating them.
Contradictions
(more...)
- A contradiction involving a
single "thing" redefines its variable value, and undefines
any dependent variable values.
- A contradiction
involving
multiple "things" is accepted, but with a warning that the
equation is "Overdetermined, and the system is
Inconsistent". It must be resolved for results to be
valid.
- A contradiction
can be resolved by removing the inconsistent equation.
- A contradiction can be resolved by redefining or clearing one
or more contradictory variables.
- AutoMathic does not automatically do anything more than detect
and report inconsistency.
Indirect References via Pronouns
(more...)
- Leading pronouns in a
noun phrase are ignored. Differentiate noun phrases with
something other than leading pronouns.
- In AutoMathic, pronouns refer to
nouns, not necessarily entire noun phrases.
- In AutoMathic, pronouns refer to the most recent noun the user
referred-to, or...
- ... Pronouns refer to the
most recent answer provided by AutoMathic.
- Simple follow-up questions that use a pronoun to refer to the
last result can be used to do a calculation bit-by-bit.
- Nouns introduced by AutoMathic, pseudo-nouns (Pi, e, etc.),
and "generic" nouns (e.g. "number", "amount", "portion", etc.)
do not overshadow the user's nouns as referents of a pronoun.
Follow-up Questions (more...)
- Additional dialogue unrelated to the current situation should
be done in a different AutoMathic session.
- Simple follow-up questions that use a pronoun to refer to the
last result can be used to do a calculation bit-by-bit.
- "No Change" follow-up
questions simply ask for new information without changing
anything.
- "Simple Change"
follow-up questions simply change one or more variables.
- "Simple Change" follow-up questions may require the user to
redefine one or more independent variables if they got undefined
in the process.
- The "lock" kernel
command can be used before a Simple Change to prevent
independent variables from being automatically undefined.
- "Complex Change"
follow-up questions change one or more existing equations.
- "Complex Change" follow-up questions usually create
contradictions that MUST be resolved.
- Retracting an
existing equation must be done using the Kernel Mode "remove" command.
- Use the Manual or Automatic method to redefine or derive
consistent variable values.
- After a Complex Change, you may need to re-state your request
to get the consistent and correct answer.
- "No Change" and "Simple Change" follow-up
questions are always safe to ask.
- It may be better to avoid Complex changes entirely and simply
restate the problem (with the changed assumptions) in a new
AutoMathic session.