logo

Expression of type Equals

from the theory of proveit.numbers.absolute_value

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprRange, Variable, r, theta
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Abs, Exp, Mult, Neg, e, i, one, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [Abs(r), Abs(Exp(e, Neg(Mult(theta, i))))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
|\left(\left|r\right|, \left|\mathsf{e}^{-\left(\theta \cdot \mathsf{i}\right)}\right|\right)| = |\left(1, \ldots, 2\right)|
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10
8Operationoperator: 12
operand: 17
9Operationoperator: 12
operand: 18
10ExprRangelambda_map: 14
start_index: 15
end_index: 16
11ExprTuple17
12Literal
13ExprTuple18
14Lambdaparameter: 22
body: 22
15Literal
16Literal
17Variable
18Operationoperator: 20
operands: 21
19ExprTuple22
20Literal
21ExprTuple23, 24
22Variable
23Literal
24Operationoperator: 25
operand: 27
25Literal
26ExprTuple27
27Operationoperator: 28
operands: 29
28Literal
29ExprTuple30, 31
30Variable
31Literal