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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 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 = [r, Exp(e, Neg(Mult(i, theta)))]), 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(r, \mathsf{e}^{-\left(\mathsf{i} \cdot \theta\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
8Variable
9Operationoperator: 11
operands: 12
10ExprRangelambda_map: 13
start_index: 14
end_index: 15
11Literal
12ExprTuple16, 17
13Lambdaparameter: 21
body: 21
14Literal
15Literal
16Literal
17Operationoperator: 19
operand: 22
18ExprTuple21
19Literal
20ExprTuple22
21Variable
22Operationoperator: 23
operands: 24
23Literal
24ExprTuple25, 26
25Literal
26Variable