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Expression of type Equals

from the theory of proveit.physics.quantum.QPE

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.logic import Equals
from proveit.numbers import Exp, Mult, Neg, frac, one, two
from proveit.physics.quantum.QPE import _t
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Mult(frac(one, two), _t)
expr = Equals(Exp(Exp(two, sub_expr1), Neg(one)), Exp(two, Neg(sub_expr1)))
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())
(2^{\frac{1}{2} \cdot t})^{-1} = 2^{-\left(\frac{1}{2} \cdot t\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: 10
operands: 5
4Operationoperator: 10
operands: 6
5ExprTuple7, 8
6ExprTuple23, 9
7Operationoperator: 10
operands: 11
8Operationoperator: 13
operand: 22
9Operationoperator: 13
operand: 15
10Literal
11ExprTuple23, 15
12ExprTuple22
13Literal
14ExprTuple15
15Operationoperator: 16
operands: 17
16Literal
17ExprTuple18, 19
18Operationoperator: 20
operands: 21
19Literal
20Literal
21ExprTuple22, 23
22Literal
23Literal