logo

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(Mult(one, Exp(Exp(two, sub_expr1), Neg(one))), Mult(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())
\left(1 \cdot (2^{\frac{1}{2} \cdot t})^{-1}\right) = \left(1 \cdot 2^{-\left(\frac{1}{2} \cdot t\right)}\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: 20
operands: 5
4Operationoperator: 20
operands: 6
5ExprTuple26, 7
6ExprTuple26, 8
7Operationoperator: 14
operands: 9
8Operationoperator: 14
operands: 10
9ExprTuple11, 12
10ExprTuple27, 13
11Operationoperator: 14
operands: 15
12Operationoperator: 17
operand: 26
13Operationoperator: 17
operand: 19
14Literal
15ExprTuple27, 19
16ExprTuple26
17Literal
18ExprTuple19
19Operationoperator: 20
operands: 21
20Literal
21ExprTuple22, 23
22Operationoperator: 24
operands: 25
23Literal
24Literal
25ExprTuple26, 27
26Literal
27Literal